Editing techniques - Silencing the drums

Recently I have been studying the art of making drum cover videos. But there's one problem I'm finding very hard to conquer...
I just don't understand how people manage to mute the sound of the drumming in tracks there covering. It's a real problem seeing as how I don't always playing exactly the same as the drummer on the track and it seems most others have found a solution.
So please, help a brother out? :p