Well, as painful as it may be to realize, you are not responsible for this guy. You cannot make him stop cutting, and you should NEVER date someone just to make them feel better. That's not fair to either of you, and will make the situation worse in the long run.
You've been a supportive friend by encouraging your friend to get counseling, but that's really something he has to want. It won't work unless he wants it to.
I would suggest going to the counselor on your own; let them know what your friend has been doing. Anyone self-harming or thinking of suicide should automatically get some support - let the counselor know how serious the situation is, and then step back.
You can only be upfront and honest with your friend. If he knows you care for him but have no interest in dating him, it can help him move on. If he is getting mixed signals, it could be adding to his confusion.
Whatever you are doing, however, please remember that it is HIS decision to react in such a harmful manner. You are not responsible for his mistakes.