‘Asma bint Marwan: Did the Prophet Order Her Killing?
Question

My question is about the death of ‘Asma bint Marwan. People speaking against Islam say that she was killed on the order of the Prophet Muhammad in a very brutal way, and this indicates, according to some, the Messenger of Allah’s lust for power in Yathrib. It would be highly appreciated if this topic is explained so that I can answer these people how benevolent the Messenger of Allah was.
Praise be to Allah.Prophet Muhammad: A mercy to the world
Allah, may He be exalted, has told us in His Noble Book that He only sent His Messenger Muhammad (blessings and peace of Allah be upon him) as a mercy to all people. Allah, may He be glorified, says (interpretation of the meaning):
“And We have sent you (O Muhammad) not but as a mercy for the ‘Alamin (mankind, jinns and all that exists).” [al-Anbiya’ 21:107].
“The one who accepts this mercy and gives thanks for this grace will be blessed in this world and in the Hereafter; the one who rejects it and denies it will be a loser in this world and in the Hereafter.” (Tafsir Ibn Kathir, 5/385)
Al-Hakim narrated in al-Mustadrak (100) that Abu Hurayrah said: The Messenger of Allah (blessings and peace of Allah be upon him) said: “O people, I am but a bestowed mercy.” (Classed as sahih by al-Albani in Sahih al-Jami‘, 2345)
How Prophet Muhammad treated his enemies
The Prophet (blessings and peace of Allah be upon him) is the one who pardoned all of Quraysh , even though they had let him down, opposed him, expelled him, waged war against him and incited the Arabs against him. When he conquered Makkah, he pardoned them and did not punish them or take revenge on them for their bad treatment .
He is the one who pardoned the Jewish woman who had poisoned the mutton for him. al-Bukhari (2617) and Muslim (5834) narrated from Anas ibn Malik (may Allah be pleased with him) that the Jewish woman brought the Prophet (blessings and peace of Allah be upon him) some poisoned mutton and he ate some of it. Then she was brought to him and it was said: Will you give us permission to execute her? He said: No.
‘Aishah (may Allah be pleased with her) said: The Messenger of Allah (blessings and peace of Allah be upon him) never took revenge for his own sake, unless one of the sacred limits of Allah had been transgressed, then he would take revenge for the sake of Allah. (Narrated by al-Bukhari (6126) and Muslim (2327)
Al-Bukhari (4838) narrated from ‘Abdullah ibn ‘Amr ibn al-‘As (may Allah be pleased with him) concerning this verse in the Quran – “O Prophet (Muhammad)! Verily, We have sent you as witness, and a bearer of glad tidings, and a warner” [al-Ahzab 33:45] – that he said: In the Torah it says: O Prophet! We have sent you as a witness and as a bearer of glad tidings, a saviour to the unlettered. You are My slave and My Messenger, and I have named you al-Mutawakkil (the one who puts his trust solely in Allah). He is not coarse or uncouth, shouting in the marketplace; he does not repay evil with evil, rather he overlooks and forgives.
The reports that speak of his patience in putting up with annoyance, and his forgiveness and tolerance, his not holding things against people and his returning evil with good are innumerable. These people only want to undermine the status of the Prophet (blessings and peace of Allah be upon him) as a sign of their increase in kufr and because of the jealousy, resentment and hatred they have in their hearts, and because they hope and wish to extinguish the light of Allah. “But Allah will complete His Light even though the disbelievers hate (it).” [as-Saff 61:8].
Prophet Muhammad forbade the killing of women
It is proven that the Prophet (blessings and peace of Allah be upon him) forbade the killing of women. Abu Dawud (2669) narrated that Rabah ibn Rabi‘ said: We were with the Messenger of Allah (blessings and peace of Allah be upon him) on a campaign, and he saw the people gathered around something. He sent a man to find out what they were looking at, and he came back and told him that it was a woman who had been killed. He said: “Such a one could not have been a fighter.” Khalid ibn al-Walid was leading the vanguard of the army, so he sent a man to him and said: “Tell Khalid: Do not kill any woman or hired worker.”
Degree of reports  about the killing of `Asma bint Marwan
As for the report about the slaying of ‘Asma bint Marwan that is propagated by these liars, it is a fabricated report. It was narrated by al-Qadai in Musnad ash-Shihab (856), al-Khatib in at-Tarikh (13/99), Ibn ‘Asakir in his Tarikh (51/244), and Ibn ‘Umar al-Harbi in his Fawaid (50), all via Muhammad ibn al-Hajjaj al-Lakhami Abu Ibrahim al-Wasiti from Mujalid ibn Sa‘id from ash-Sha‘bi from Ibn ‘Abbas, who said:
A woman from Banu Khatamah wrote poetry lampooning the Prophet (blessings and peace of Allah be upon him), and news of that reached the Prophet (blessings and peace of Allah be upon him) and upset him. He said: “Who will deal with her for me?” A man from among her people said: I will, O Messenger of Allah! She was a seller of dates, so he went to her and said to her: Do you have any dates? She said: Yes. So she showed him some dates, and he said: I want something better than this. So she went inside to show him and he followed her and looked right and left, but he did not see anything except a small table, and he kept hitting her head with it until he killed her. Then he went to the Prophet (blessings and peace of Allah be upon him) and said: O Messenger of Allah, I have taken care of her for you. The Prophet (blessings and peace of Allah be upon him) said: “The validity of what you have done is something that no one could dispute.”
This woman was ‘Asma bint Marwan.
“This is an invalid isnad and a fabricated report that was narrated by Muhammad ibn al-Hajjaj of whom al-Bukhari said: His hadith is to be rejected. Ibn Ma‘in said: (He is) an evil liar. Ad-Daraqutni said: (He is) a liar; and on one occasion he said: He is not trustworthy.” (Mizan al-I‘tidal, 3/509)
Ibn ‘Adiyy said: 
“Muhammad ibn al-Hajjaj fabricated the hadith about the woman who used to lampoon the Messenger of Allah (blessings and peace of Allah be upon him), according to which when she was killed he (allegedly) said: “The validity of what you have done is something that no one could dispute.” (Al-Mawdu‘at by Ibn al-Jawzi 3/18)
This hadith was also mentioned by Shaykh al-Albani (may Allah have mercy on him) in ad-Da‘ifah (6013); he said it is fabricated (mawdu‘).
It was narrated by al-Waqidi in al-Maghazi (p. 173) and via him by al-Qadai (858):
“‘Abdullah ibn al-Harith told me, from his father, that ‘Asma bint Marwan, from Banu Umayyah ibn Zayd, was married to Yazid ibn Zayd ibn Hisn al-Khatmi. She used to revile the Prophet (blessings and peace of Allah be upon him), criticise Islam and incite people against the Prophet (blessings and peace of Allah be upon him). When news of what she said and her incitement of the people reached ‘Umayr ibn ‘Adiyy ibn Kharashah ibn Umayyah al-Khatmi, he said: O Allah, I make a vow to You that I shall kill her if You grant a safe return to Madinah to the Messenger of Allah (blessings and peace of Allah be upon him) – as the Messenger of Allah (blessings and peace of Allah be upon him) was in Badr at that time. When the Messenger of Allah (blessings and peace of Allah be upon him) came back from Badr, ‘Umayr ibn ‘Adiyy came to her in the middle of the night and entered upon her in her house when she had a group of her children sleeping around her, including an infant who was still being breastfed. He reached out to touch her and found the infant whom she was breastfeeding. He pushed the child aside then he plunged his sword into her chest until it came out of her back. Then he went out and prayed Fajr with the Prophet (blessings and peace of Allah be upon him) in Madinah. When the Prophet (blessings and peace of Allah be upon him) finished praying, he looked at ‘Umayr and said: Did you kill the daughter of Marwan? He said: Yes, may my father be sacrificed for you, O Messenger of Allah.
‘Umayr was afraid that the Prophet (blessings and peace of Allah be upon him) would not approve of his killing her, so he said: Is there any sin on me for that, O Messenger of Allah? He said: “The validity of what you have done is something that no one could dispute.” And this is the first time I heard this phrase from the Prophet (blessings and peace of Allah be upon him). ‘Umayr said: The Prophet (blessings and peace of Allah be upon him) turned to those who were around him and said: “If you want to see a man who supported Allah and His Messenger, then look at ‘Umayr ibn ‘Adiyy.” 
“This is a worthless isnad. Imam Ahmad said concerning al-Waqidi – whose name was Muhammad ibn ‘Umar ibn Waqid – : He is a liar; he alters hadiths. Ibn Ma‘in said: He is not trustworthy. On one occasion he said: His hadith is not to b written down. Al-Bukhari and Abu Hatim said: He is matruk (rejected). Abu Haatim and an-Nasai said: He fabricates hadith. Ibn ‘Adiyy said: His hadiths are odd and problematic. Ibn al-Madini said: al-Waqidi fabricates hadith.” (Mizan al-I‘tidal, 3/663)
An-Nasai said: 
“The liars who are known for fabricating hadith are four: Ibrahim ibn Abi Yahya in Madinah, al-Waqidi in Baghdad, Muqatil in Khorasan and Muhammad ibn Sa‘id in Syria.” (Tahdhib at-Tahdhib, 9/163)
And Allah knows best.