How to tell groomsman he is no longer welcome at the wedding?

Yeah, this seems like a huge overreaction on his end, I could see him being hurt or disappointed, but assuming you guys told him gently that he wouldn't be giving a speech this is too much.

I'd suggest reaching out with the intent to see if he has calmed down. Maybe offer a toast at the rehearsal dinner or something. But if he is still heated and upset they you might have to decide to uninvite him, which will definitely ruin the friendship (I just had to uninvite a bridesmaid so I know how it feels!) Just make sure you'd be okay with losing him as a friend if you choose to uninvite.

It sounds like his speech is definitely something you'd want to skip regardless of whether there is time or not. It's one thing to add in a little bit of humor to the speech, but a totally different thing for him to want to make "jokes" that are offensive and humiliating to the point where he anticipates that they will potentially split up your new marriage. The speech is also supposed to be centered around you and your new husband, not roasting your families. If you choose to let him give a speech (whether at the reception or rehearsal dinner), I would strongly recommend reading it ahead of time and request that he remove anything offensive beforehand. Your fiance might want to reach out to him one more time to see if he's calmed down from everything (I still don't really understand why he's even this upset over not being able to give a speech), and if not, give the groomsman the opportunity to step down if your fiance does not want to include him anymore. It doesn't seem like he's being supportive of you and your fiance.

He sounds like a jerk who might try to push his way into the spotlight anyway, even after you told him he can't give a speech. I would call and say something like you heard he was expecting an apology, you aren't giving him one, and that after his reaction you feel it might be best if he just skip the wedding altogether. He may not speak to you again, but it doesn't sound like that would be a big loss.