Blow somebody off means to leave them without notice. To not attend something without telling someone you were not attending. Let me give an example: Julie invited me to the party. However, because John asked me to go to the movies with him, I blew Julie (and her party) off.

To disregard someone in an uncaring way. Like, you ask you friend Bob for help... but he just waves his hand and says "Yeah, whatever; I don't have time for that right now" and leaves -- Bob just totally blew you off.

放鸽子