Should I cut off one of my friends?
That sounds like a big deal. What made you want to cut the person off?
I was thinking they might make some drama, and I don't want to be bothered.
While sometimes you may feel like friendships are a burden, you spent so much time working on this relationship that throwing it all away would hurt both of you. If you dislike the drama then you should let them know and maybe you could all work through it.
No. I am sure he will drift away from me anyways.
Are you sure? If you plan to just block and simply cut him off, then it probably wouldn't hurt to at least try and figure things out. I am sure the person will feel abandoned and might end up stalking you, so you might as well take the first step and reach out.