these are three degrees of rudeness and fun at other expense.
Joke- likely some level of rudeness, BUT- the person who is the topic of a joke may not (probably is not) hearing the joke. It he person may be not a real person (but rather a character type- a doctor /lawyer/priest/poor man/rich man/woman....) or may be a well known person such as a politician or celebrity person.
Tease- to joke about someones flaw while they are there. A tease may be insulting, yet the person teasing may or may not realize how the teasing is effecting the person. It may be that the teaser (person teasing) thinks that the person being teased understands it as a friendly joke, even though they may be wrong about that. The person may feel mocked.
Mock- To insult a person intentionally (with the goal of being nsulting) in a way that points out a specific flaw or unusual facet of a persons character. It may or may not be done in a mimicking way. Of the three, this is the most insulting in my opinion.