What would you do if your son did this?

That would be a horrific situation

I would start by breaking my belt on him, literally bust his ass until it breaks, while the wife gets her to the hospital

Likely therapy and/or juvenile detention after that, you don't hurt women, especially young ones, much less break their finger

look for family therapy :(

Being deaf isn’t an excuse. If he’s violent purposely within the family he can’t live at home.

Kick his butt . There is never an excuse for violence of anysort .

I would try to talk to him. (Try to) approach him with love rather than a punishment that will feed his resentment even further.
16 is a terrible age for some. Not that he's excused though. You definitely need to talk this out.

Punishment. He goes with you to Dr. He pays for any medical cost. Maybe therapy if more there.

I'd ground him until I got tired of it.