Laughing at someone could be laughing at someone's joke, or if they fall down, you're laughing at their accident. Mockery is teasing someone, for example "how did you fall down? You must have no brains" Not in a joking way, but intending to be mean. If I didn't explain clearly please let me know :)

It is very common to say , for example, "John laughs at his friend's strange behaviour" However, sometimes we also use the term mockery. An example with "mockery", is "John mocks his boss's behaviour" Sometimes , friends might laugh at each other, but mocking someone is usually considered an insult. I hope this helps Casey

First of all, "mockery" is a noun. Between "to mock somebody" and "to laugh at somebody", I would say "mock" is more aggressive, more ill-spirited.