Blow Up someone means the last one. to lose one’s temper.
1. To come into being: A storm blew up.
2. To fill with air; inflate: blow up a tire.
3. To enlarge (a photographic image or print).
4. To explode: bombs blowing up.
5. To lose one's temper.
I came up to this word looking at first page of yahoo. A story about one of David Letterman’s guests.
and the title was:
Disgruntled actress launches into an angry rant when David asks about her ex-hubby.» Buzzed-about harsh words