What is the origin of “pissed off”, to mean being mad, angry, etc.?
KnK
I don’t know but I’d much rather be pissed off than pissed on. 
Here in the UK, to be pissed off is to be fed up or annoyed, and to be pissed is to be drunk. In either case, hlanelee is entirely correct.
In fact, the word piss and its variant forms are a very flexible part of the language around here…deftly demonstrated by owlstretchingtime in this in this finely crafted excerpt from this thread about swearing.
As you can see, to piss off can also mean to depart - either describing ones own departure, or as an instruction for another to depart. It’s a shame he didn’t squeeze in a reference to it pissing down (with rain). Not that any of this actually answers your question, but an interesting little aside, I think.
And the best place for a pisspot to go on the piss until he’s pissed is at a piss-up.
Oh c’mon. You guys are just taking the piss.
Another potentially informative thread pissed up against the wall.
And I think Sqwerticus is trying to piss in owlstretchingtime’s pocket.
Now I am pissed off.
Hey, what do you reckon the origin of that phrase ‘pissed off’ might be?
Sensible answers only from now on.
There now. That’s the wall thats been pissed up against sorted out.
So, can we safely say this has degenerated into a pissing contest?
C’mon you blokes, this humour is as weak as piss. It really is piss-poor.
Well, isn’t that just a pisser.
And you’re being a bit pissy about it, Loaded.
We can safely say that GQ is awash in people who don’t know shit from shinola.
Random House’s excellent word site, Mavens’ Word of the Day which is now defunct, can quite often lend a hand, which they do it this case.
According to them, it appears in and about WWII.
Awwww. Now **samclem[\b] has pissed on our firework.
Life is like a pubic hair on a toilet seat.
Sooner or later…