ape

noun

any of various primates with short tails or no tail at all
person who resembles a nonhuman primate

anthropoid
someone who copies the words or behavior of another

copycatimitatoremulatoraper

verb

to represent in or produce a caricature of
“Everyone cracks up when I ape the way that you lecture us.”
caricature
to imitate uncritically and in every aspect
“My younger siblings ape my behavior.”