I'm amazed by this rhetoric of how Islamic State is not really Islamic. This is ridiculous and insensitive. Men are leaving their homes and safety for the sake of Islam as they understand it within the Islamic State.
And when the people of the IS cut off the heads or crucify those whom they consider to be enemies of Islam, they are simply emulating Muhammad, the ideal man.
Here is where the Qur'an enjoins crucifixion:
“Indeed, the penalty for those who wage
war against Allah and His Messenger and strive upon earth [to cause]
corruption is none but that they be killed or crucified
or that their hands and feet be cut off from opposite sides or that
they be exiled from the land. That is for them a disgrace in this world;
and for them in the Hereafter is a great punishment.” — Qur’an 5:33
And here is where the Prophet is told to decapitatet (ie, strike on the neck with a sword) those who are enemies of Islam, specifically in the context of the Battle of Badr:
[Remember] when your Lord
inspired to the angels, "I am with you, so strengthen those
who have believed. I will cast terror into the hearts of
those who disbelieved, so strike [them] upon the necks and
strike from them every fingertip." -- Qur'an 8:12
So please, understand that the men of the Islamic State have a solid argument on their side that their actions are indeed Islamic and they are merely imitating the Prophet.