You need to learn about phrasal verbs:
http://grammar.ccc.commnet.edu/grammar/verbs.htm#phrasal (Be sure to click on the word HERE to see very useful lists of these verbs.)
And here are several dictionary definitions of this particular phrasal verb, "break up":
Let me know if you have more questions about phrasal verbs or this phrasal verb in particular.
English is a great language. You can chop a tree down, and then chop it up.