I don't know about puns but I once saw a documentary about a deaf and mute married couple who had a baby. The interesting thing was that the baby started "babbling" with its hands. Can't remember if it was deaf and/or mute as well.
I know historically “deaf and dumb” meant deaf and mute, but, at least in the classes I took in college, I was told we don’t use that terminology anymore, for hopefully obvious reasons.
This isn’t replacing a euphemism with another one. Dumb has a completely different meaning that’s not even close to ‘cannot speak’, while ‘mute’ conveys exactly that.