You could use mimes in the first, but in both examples mimics would be the better word. He mimics films and the group guesses the title.
He mimics a film and others guess what it is.
Mime could be used as a noun and mimes can be used as a verb. Mimics is the act of copying or replicating an action or idea, so it would be a better verb. Like a Mime mimics. A Mime mimes. The first makes more sense.