They are simply implementing Islamic law in the Islamic State. The caliph Umar, one of Muhammad’s closest companions, maintained that the punishment of stoning for adultery (this story doesn’t specify the method of punishment, but the outcome of the punishment is the same in any case) was originally in the Qur’an:
‘Umar said, “I am afraid that after a long time has passed, people may say, “We do not find the Verses of the Rajam (stoning to death) in the Holy Book,” and consequently they may go astray by leaving an obligation that Allah has revealed. Lo! I confirm that the penalty of Rajam be inflicted on him who commits illegal sexual intercourse, if he is already married and the crime is proved by witnesses or pregnancy or confession.” Sufyan added, “I have memorized this narration in this way.” ‘Umar added, “Surely Allah’s Apostle carried out the penalty of Rajam, and so did we after him.” (Bukhari, vol. 8, bk. 82, no. 816)
“Allah’s Apostle” is, of course, Muhammad, who did indeed carry out stonings. Here is the hadith in which he challenges the rabbis about stoning, and in which there is amidst the barbarism and brutality a final act of love and compassion:
The Jews came to Allah’s Apostle and told him that a man and a woman from amongst them had committed illegal sexual intercourse. Allah’s Apostle said to them, “What do you find in the Torah (old Testament) about the legal punishment of Ar-Rajm (stoning)?” They replied, (But) we announce their crime and lash them.” Abdullah bin Salam said, “You are telling a lie; Torah contains the order of Rajm.” They brought and opened the Torah and one of them solaced his hand on the Verse of Rajm and read the verses preceding and following it. Abdullah bin Salam said to him, “Lift your hand.” When he lifted his hand, the Verse of Rajm was written there. They said, “Muhammad has told the truth; the Torah has the Verse of Rajm. The Prophet then gave the order that both of them should be stoned to death. (‘Abdullah bin ‘Umar said, “I saw the man leaning over the woman to shelter her from the stones.” (Bukhari, vol. 4, bk. 56, no. 829)
Even the monkeys practiced stoning, according to another hadith:
During the pre-lslamic period of ignorance I saw a she-monkey surrounded by a number of monkeys. They were all stoning it, because it had committed illegal sexual intercourse. I too, stoned it along with them. (Bukhari, vol. 5, bk. 58, no. 188)
Muhammad’s example is, of course, normative for Islamic behavior, since “verily in the messenger of Allah ye have a good example for him who looketh unto Allah and the Last Day, and remembereth Allah much” (Qur’an 33:21).
“Islamic State militants stone man to death in Iraq -witness,” Reuters, August 22, 2014 (thanks to Twostellas):
BAGHDAD, Aug 22 (Reuters) – Islamic State militants in Iraq stoned a man to death in the northern city of Mosul after one of their courts sentenced him to die for the crime of adultery, a witness said on Friday.
The stoning, which happened on Thursday, was the first known instance of the punishment by al Qaeda offshoot Islamic State militants in Iraq, although it had been reported previously in Syria.
Members of the hardline Sunni group, which seized Mosul in June and also controls swathes of territory in neighbouring Syria, have shot, beheaded and crucified prisoners and blown up and bulldozed Shi’ite mosques.
The United States began air strikes on Islamic State positions in Iraq this month, and in retaliation the group published a video of one of its black-clad fighters beheading U.S. journalist James Foley.
A taxi driver who said he saw Thursday’s stoning in Mosul said he stopped to find out what was happening when he noticed a crowd gathering and about 20 Islamic State vehicles parked nearby.
Some militants were gathering sharp pieces of rock while another held a video camera, he said.
Eventually, the militants brought a handcuffed young man from one of the vehicles, made him sit down on the ground, and began pelting him with rocks, the witness said. Some in the crowd turned away as the man cried, “I did nothing,” he said.
“I had a glance at this person, I saw some of the stones hitting his head, and then I turned away,” the witness said, asking not to be named out of fear of retaliation.
After about 15 minutes, the militants told the crowd the stoning was finished, and an ambulance took away the body. A source at the morgue in Mosul confirmed the death of the man and said his identification showed he was 30 years old.
The stoning was also reported on local media. Neither the witness’s nor the media’s accounts could be independently corroborated.
In July, activists reported Islamic State militants stoned two women to death for adultery in Syria’s Raqqa province, which borders Turkey and is a major stronghold for the group.
U.S.-trained Iraqi government forces, which largely fled when Islamic State militants arrived from Syria, have not been able to push their way back into Mosul, where the group has imposed its extreme ideology, even destroying statues of famous Iraqi poets it deems as un-Islamic.
The witness said the stoning was widely discussed on the streets of Mosul, which was seen as one Iraq’s most tolerant cities before falling under the grip of the group, which is made up of Iraqis and other Arabs as well as foreign fighters.
Many sects and ethnic groups lived in harmony in the region. Now all sides are just trying to survive the reign off the Islamic State.
“Most of the people were not surprised, because this is typical of their behaviour,” he said, referring to the militants.