I've decided recently that one of my friendships has deteriorated to the point where it is in my best emotional interest to cut it off. I can't stop being angry at him for taking advantage of my friendship but I'm too much of a coward to tell him I never want to speak to him again.
Has anyone ever been in a similar situation? Does anyone have any advice for getting over the end of a close friendship?

Well if you truly believe that it is in your best interest to end this relation ship then it is in your best interest to tell him that you never want to speak to him again. This may seem hard and is clearly something that you really do not want to do, but if it's what you have to do in order to move on then I highly recommend it.
However if you simply cannot bring yourself to do this, the only other advice I can give you is to completely cut out your contact with him(do not message, email, call and so on). Although if you see him around do not go out of your way to avoid him as this could lead to far more awkward situations.

I've been in a similar situation myself where a close friend of mine betrayed me and he was involved a group of friends very close to me. In this particular situation, the approach I took was to make my feelings clear on how I felt about him (or what he did) without generating any animosity or enimity between us. So now we are no longer friends but that does not stop us from being acquaintances and from talking or interacting when we do meet. This approach helped us prevent any undue awkwardness as we shared largely the same group of friends.

If the friend you are referring to is not someone you would meet regularly you could also blacklist him completely. However, in my experience I have found it is better not be enemies even if you can't be friends unless the person has caused you some grevious and uncalled for harm .