Does it sound like a good idea for me to exclude a guy from our friend group?
Why do you think you should exclude him?
I don't think he adds any real value to the group. He's no longer a true friend of mine.
While you are within your right to kick him from the group, that's pretty rude of you to do so.  I think it should be a decision for the whole group to make!
I've decided it's best for the group, and that guy will just drag us down with him anyhow.
If you truly think that he will drag you down, then you need to speak with the rest of your friends first and see how they feel about it. Then, if they agree, you should speak with him in private and explain that he needs to change his ways if he wants to spend time with you still. It's very callous to just cut someone out of a group.