A “parody” is an imitation of a person, place, or thing, done in order to poke fun at them. Sometimes this is done just to be humorous, but other times a parody can be sharper, mocking someone’s mannerisms in a way intended to be hurtful.
Example: “Jane’s parody of her French professor’s lectures had everyone laughing, but when the teacher walked into the classroom, she was not amused.”