Kill, especially by gunshot or explosion. For example, The unit reported that the whole village was blown away. This usage became particularly widespread in the 1960s, during the Vietnam War. [Slang; early 1990s]
Overcome easily; defeat decisively. For example, Ann said the test would be easy; she would just blow it away, or Jim was sure his crew could blow away their opponents. [Slang; 1960s] Also see blow off, def. 5.
Impress greatly, overwhelm with surprise, delight, or shock, as in That music really blew me away. [Slang; c. 1970] Also see blow one's mind.