Acording to The Dictionary of Contemporary Slang by Tony Thorne this usage emerged at the time of World War II

piss off

to piss off

1. To go away, rude:
   Brother: How are you this morning? *ironicly* Enjoy yourself last night?
   Me (hung over):*genuinely* Piss Off!
2. to anger someone
   Don't piss off the cook, he'll shit in your pie!
   or
   Stop telling that bouncer where he went wrong in life, you're pissing him off, he weighs 20 stone and looks like he eats little children for breakfast!