Looking for drama with main cast that has hearing or speaking disability

The way I understand your question, is that you're looking for an actor or actress (who have played lead roles) with hearing or speaking difficulty. Unfortunately I don't know any. 

However, I do know a movie with a main character with hearing (and thus also speaking) disability, which is Hitsudan Hostess (j-movie), which I can't recommend enough! It's a beautiful story.
There's also Hear Me (tw-movie). I haven't watched it yet, but I've heard that it's really good.

"Love song" the main lead has a problem with heavy stuttering and throughout the drama tries to get better with her speaking

Can You Hear My Heart

Dream High has a character who goes deaf kinda :)

Kiseki no Hito is one of my faves. The little girl is blind and deaf