Webster Collegiate says 'blow off' means 'ignore' or 'to refuse to take notice of'.
But what about 'blow off the exam'?
Somebody told me 'blowing off the exam' means not taking the exam. But is it possible that it means not taking the exam seriously by, say, watching TV all night before the exam, and come to take it the next day anyway?
"Blowing off the exam" could mean either of these. Basically, the person is saying thy didn't take the exam seriously, whether they didn't take it or they didn't prepare for it. The phrase itself is not definative.