1 to stop illegal or dishonest activity in a place or organization:
2 to stop or limit the violence, sex, or bad behaviour shown or contained in programmes or books, magazines, etc., to make them more acceptable:
Some people think that television should be cleaned up.
3 to stop illegal and dishonest activity in a company, system, etc.:
4 to remove harmful substances or chemicals from a place or the environment:
clean up pollution/contamination/waste $250 million was spent on cleaning up groundwater contamination at the former factory's site.