What does it mean to dream about cutting up a person's body?

It means you don't like that person very much. Violent actions (stabbing, slicing, cutting, shooting, bludgeoning) perpetrated against another in a dream usually indicates extreme dislike/hatred toward the individual.

Some believe mutilation/killing (and other acts of violence) in dreams can actually prevent real-life altercations with the individual dreamed about. In other Words, the satisfaction (if any) gained through the act in the dream, is realized physically/emotionally in the wakened state.