To Blow Away
transitive verb, godan verb
You know that 吹く is "to blow" and that 飛ばす is "To let fly." So, if you use your blowing to let something fly, you are going to blow away it.
The reading comes from 吹く and 飛ばす, put together.
パーティーに行って、憂鬱なんて吹き飛ばしちゃおうぜ。
Let’s go to the party and brush off your depression.