It is alleged that Asma bint Marwan was assassinated by Prophet Mohammad (p) because she insulted and wrote poetry against him. The story has been reported by some biographers on the Prophet’s life, who collected stories without verifying if the story is true or false, hundreds of years after the Prophet’s demise.
This story has not been recorded by any of our most authentic Hadith collections. This is similar to the story of Jesus killing a child in the Gospel of Thomas, and critics try to force the story upon Christians that they have to accept it as evidence that Jesus was a murderer.
However, no credible scholar (Christian or non-Christian) would use this incident as true even though the Gospel of Thomas is dated earlier than the Gospel of John. This is the same case with the story of Asma as well – it is a fake story, forged in order to degrade and vilify the Prophet of Islam as a barbaric man.
The sources used by critics are laughable. If one were to read the source of what is said and how the alleged killing was carried out, one straight-away would notice the story is a lie. Lets’s read;
“She used to revile Islam, offend the prophet, and instigate the people against him. She composed verses. Umayr Ibn Adi came to her in the night and entered her house. Her children were sleeping around her. There was one whom she was suckling. He searched her with his hand because he was blind, and separated the child from her. He thrust his sword in her chest till it pierced upto her back. …” 
So the Prophet (p) sent Umayr, a blind man, to carry out an assassination? Umayr must have been a special kind of blind man to go roaming around and enter a property while Asma is awake while breastfeeding and her not noticing nothing, let alone eventually killing her. How did the blind man, Umayr, find her at the right place and stabbed her without detection?
Moreover, the claim that the Prophet (P) got her assassinated just because of some poetry insulting him is false. The reason the story is fallacious is because we have in our most authentic sources Prophet Muhammad’s (p) wife Aisha reporting that he never took revenge on anyone for his own sake:
Narrated `Aisha: Allah’s Messenger never took revenge for his own self in any matter presented to him till Allah’s limits were exceeded, in which case he would take revenge for Allah’s sake. (Sahih al-Bukhari: Volume 8, Book 82, Hadith 836)
Sunan Abi Dawud
`A’ishah said: the Messenger of Allah was never given his choice between two things without taking the easier (or lesser) of them provided it involved no sin, for if it did, no one kept farther away from it than he.
And the Messenger of Allah never took revenge on his own behalf for anything unless something Allah had forbidden has been transgressed, in which event he took revenge for it for Allah’s sake. (Sunan Abi Dawud: Book 42, Hadith 4767)
‘Aishah reported: Whenever the Prophet was given a choice between two matters, he would (always) choose the easier as long as it was not sinful to do so; but if it was sinful he was most strict in avoiding it.
He never took revenge upon anybody for his own sake; but when Allah’s Legal Bindings were outraged, he would take revenge for Allah’s sake. (Riyad as-Salihin Book 1, Hadith 641)
So, who are we to believe here, the Prophet’s wife who lived her life with him or some biographers coming hundreds of years later reporting this pseudo story on Muhammed (p)? I go with Aisha (ra).
The evidence above by Aisha shows that the story on Asma is forgery and has no bearing historically on the Prophet (p). Furthermore, the following scholars also point out that the story is fake.
THE ALLEGED ASSASSINATIONS
There were certain executions of culprits who had perpetrated the crime of treason against the Moslem Commonwealth. These executions, and certain other cases of murders not grounded on any credible evidences, are narrated by European biographers of Mohammad as assassinations committed through the countenance and connivance which he lent them.
They were about five or six in number, and they are styled assassinations from there being no trials of the prisoners by a judge and a jury, nor by any systematic court-material. The punishment of death was inflicted upon the persons
condemned, either from private enmity or for the unpardonable offence of high treason against the State, but it cannot be said, as I will hereafter show, that these so-called cases of assassinations had received the high sanction of Mohammad, or they were brought about at his direct instigation and assent for their commission.
The alleged instances are as follows:-
1. Asma-bint Marwan
2. Abu Afak.
3. Kab-ibn Ashraf
4. Sofian-ibn Khalid
5. Abu Rafi
6. Oseir-ibn Zarim
7. The attempted assassination of Abu Sofian
Before reviewing the truth and falsity of evidence in each of these cases, and showing how far the Prophet was privy to them, I will avail myself of a quotation from Mr. Stanley Lane Poole, who has remarked with his usual deep discernment and accurate judgement.
In his introduction to Mr. E. W. Lane’s selections from the Koran:
“The execution of the half-dozen marked Jews is generally called assassination, because a Muslim was sent secretly to kill each of the criminals.
The reason is almost too obvious to need explanation. There were no police or law-courts, or even courtsmartial, at Medina; some one of the followers of Mohammad must therefore be the executor of the sentence of death, and it was better it should be done quietly, as the executing of a man openly before his clan retaliation, till the whole city had become mixed up in the quarrel. If secret assassination is the word for such deeds, secret assassination was necessary part of the internal government of Medina.
The men must be killed, and best in that way. In saying this I assume that Mohammad was cognisant of the deed, and that it was not merely a case of private vengeance; but in several instances the evidence that traces these executions to Mohammad’s order is either entirely wanting or is too doubtful to claim our credence.’
The story of Asma’s murder has been variously related by the Arabian writers, and the testimonies on which it rests are contradictory and conflicting in themselves. Wakidi, Ibn Sa’d, and Ibn Hisham relate a verse strange thing about it, that she was killed by Omeir the blind at the dead of night. A blind person commits murder in a stranger’s house during nocturnal quietness, and is not arrested by any one!
Doctor Weil writes, that Omeir was a former husband of Asma, and the origin of the murder may be traced to a long-brooding and private malice. Ibn Asakar in his history (vide seerat shame) relates that Asma was fruit-seller; some person of her tribe asked her if she had better fruits she said ‘yes,’ and entered her house followed by that man.
She stooped down to take something up, the person turned right and left, and seeing that nobody was near, gave a violent blow on her head, an thus dispatched her. The historians even relate that Omeir, being offended at the verses composed by Asma, had volunteered himself of his own free-will to kill her. She might have been a sacrifice to envy or hatred by the sword of her assassin, but Mohammad really had no hand in her death.
She had made herself an outlaw by deluding the people of Medina to a breach of treaty with the Moslems, whereby the rights and jurisdictions of Jews and Moslems were definitively settled. Ibn Ishak quitly leaves unnarrated any transaction with regard to Asma. Wakidi and Ibn Sa’d do not affirm that Mohammad, being annoyed at her lampoons, said dejectedly, ‘Who would rid me of that woman?’
On the contrary, Wakidi writes, that Omeir had voluntarily swore to take her life. It is only Ibn Hisham who relates without citing his authority, that Mohammad, hearing Asma’s verses declared: ‘Is there nobody for me (i.e., to rid me) from Bint Marwan?’ This version of the story has no corroborative proofs from the earliest biographers, and we are not inclined to put any faith in it. 
Maulana Muhammad Ali
The first cases cited… is that of Asma of the tribe of Aus. She is said to have been a poetess who wrote some verses stating that the Prophet was an upstart who had slain many of their chiefs, referring to the battle of Badr. It is stated that she was brutally murdered for this abuse by a Muslim named ‘Umair, and that the Prophet not only approved of this murder but also praised Umair for the deed.
The authorities quoted are Waqidi, Ibn Hisham and Ibn Sa’d. That this is not a reliable record is shown not only by what has been stated above – that the Holy Qur’an never allowed the murder of an abuser – but also by clear directions repeatedly given by the Holy Prophet that no woman was to be killed even though she took part in actual war with the Muslims.
No less an authority than Bukhari has a chapter on the ‘Murder of women during war’ (Kitab al-Jihad) in which the following report from Ibn Umar is recorded: ‘A woman was found killed in one of the battles fought by the Holy Prophet, so the Holy Prophet forbade the killing of women and children.’
If the Holy Prophet forbade the killing of women even when they were actually accompanying the enemy forces, how could he approve or applaud the killing of a woman for simply abusing or composing some annoying verses?
Even the companions of the Holy Prophet were so well aware of his strict orders against the killing of women that when Abul Huqaiq’s wife interposed herself between them and Abul Huqaiq, they had to withhold their raised swords ‘because they remembered that the Holy prophet had forbidden the killing of a woman’ (Fath al-Bari, ch. Killing of Abul Huqaiq).
In the face of this clear testimony, none but biased mind can accept as reliable a report which relates that the Holy prophet had ordered and applauded the killing of a woman simply for the offence that she composed annoying verses. This report is undoubtedly a forgery.
The fact is this established beyond the shadow of a doubt that the Holy Prophet gave a clear interdiction against the murder of women even in wars.
In this connection, a saying of the Holy prophet has been quoted from the most reliable traditionists of Islam, the Imam Bukhari. The heading under which Bukhari quotes this saying is ‘Murder of women during wars,’ thus showing that the interdiction against the murder of women was to be observed even in wars.
Bukhari is not alone in reporting the incident and the interdiction; it is contained in all the books of the Sihah Sittah (the six reliable collections) with the exception of only one, and therefore its authenticity is beyond dispute. Moreover, their interdiction is accepted as a basic principle by later jurists.
Thus according to Malik and Auza’I, the killing of women and children is not allowed under any circumstances whatsoever, and according to Shafi’I and Kufis, a woman may be killed only when she is a combatant, while according to one authority, even when a woman is a combatant it is not lawful to kill intentionally unless she is about to kill or attack a man with the intention of killing him. (Aun al-Ma’bud, commentary on Abu Dawud, ch. Murder of women).
According to Malik and Auza’I, however, as already stated, a woman should not be killed under any condition, so much so that if a fighting force takes the shelter of women an children or takes shelter in a fort or a boat in which there are also women and children with them,
it is not lawful to shoot at or set fire to the fort or the boat (Fath al-Bari, ch. Ahl al-dar-I yabitun). In the face of these facts it is simply unthinkable that the Prophet should have ordered the assassination of a woman, under peaceful conditions, for no other fault than singing certain annoying verses. 
Credit Discover the truth
Allah knows Best
 Kitab al-Tabaqat Al-Kabir – by Ibn Sa’d, volume 2, page 30
 A Critical Exposition of the Popular Jihad (Original 1885) – Cheragh Ali Page 60 – 64
 Muhammad The Prophet By Maulana Muhammad Ali, page 199 – 201