WordNet sense 1 (an actor who communicates entirely by gesture and facial expression):

mummer, pantomimist, mimer, pantomimer

WordNet sense 2 (imitate (a person or manner), especially for satirical effect):

mimic

WordNet sense 3 (act out without words but with gestures and bodily movements only):

pantomime

WordNet sense 4 (a performance using gestures and body movements without words):

dumb show