They're actions are anything but Islamic.
I've thought a lot about what to write for this post.. but honestly, I will post a link to the 19 page "Open Letter to Baghdadi" which was compiled and signed by 126 Muslim leaders worldwide:
http://lettertobaghdadi.com/
It details, point by point why the Islamic State's actions are wrong, based on the teachings of Islam.
If you have the time, please read through the letter.