Removing the video will only cause it to become more widespread, study the Streisand effect
for the reasons why that is.
Streisand effect - Wikipedia, the free encyclopedia
Every time something like this happens there is a segment of society that immediately wants to ban things and give the government power to create more laws and crack down on our freedom. It is the very same reactionary behavior that allowed Stalin and Hitler, among others, to accomplish what they did, tyrants love to take advantage of the fear and insecurity of the people they have power over and this case is no different, those who have a desire to censor the internet and take away more of our freedom will use this case to further their perverted agenda.
Decisions about matters such as banning websites and making certain things illegal should not be made until long after events like this after people have settled down and gotten their heads about them.
Further, in the words of the great Ben Franklin:
They who would give up essential liberty to obtain a little temporary safety, deserve neither liberty nor safety.
I personally do not like gore sites but there is something I hate even more, people telling me what parts of reality I can and cannot see.
That video, while digusting beyond measure, is an unfortunate part of the reality we live in, to stick your head in the sand and deny its existence is the ultimate insult to the victim.