Why Don't We take Down Thier Web Sites?

From Fox News: Japan reacted with shock and anger Sunday after an online video was released that appeared to show Islamic State executing Japanese journalist Kenji Goto -- the apparent end to a frantic past couple of days in which officials tried negotiating to save Goto’s life.
The video, called "A Message to the Government of Japan," featured a militant who looked and sounded like a militant with a British accent who has taken part in other beheading videos by the Islamic State group...
Japanese Prime Minister Shinzo Abe expressed outrage at the video that was released on militant websites.  http://www.foxnews.com/world/2015/02/01/video-isis-beheads-japanese-journalist/
We can send a man to the moon.
We have the highest technology regarding computers and technology.
Hell, we even have Al Gore, who invented the Internet.
So, why can't we and other allies, take down these murderous thug's web sites?
Why can't we hack them and put out our messages?
If you can stop them from putting out their messages and their propaganda, then these thug killings may stop.
Maybe if the U.S. or ally put a picture of muhammad wearing a shit filled diaper instead of videos of the killings, then the killings will stop.
These thugs are murdering their hostages because of the publicity they receive, so let's shut down their web sites and try to eliminate their publicity.