Yes, you do. It is just so very hard to do but it is time. For your sake and his. Check into the laws for your state because you may have to go through the eviction process to kick him out. I found that out the hard way when we tried to make out daughter leave and the police backed her up and told us we couldn't kick her out. Even if they don't pay rent some states consider them residents and force you to go through the eviction process.
Your son may or may not find his way out on his own but letting him stay with you is obviously not making him better and it is making your life miserable. So it is time for him to go. My husband and I went to some Families Anonymous meetings and every parent there said that their adult child did not start doing better until they finally kicked them out and stopped enabling their behavior.
It took me two years of therapy to be able to let go and let God as they say in Al-Anon. Have you tried going to meetings or finding a therapist?
Keep posting. Many of us have gone through this and you will find understanding and support whatever you decide to do.
~Kathy