1958, intransitive, "go away," chiefly British; the transitive meaning "annoy (someone)" is by 1968, chiefly U.S.; from piss (v.) + off (adv.). Pissed off "angry, fed up" is attested by 1946 (Partridge says 1937); said to have been used in the military in World War II; in common use from 1970s.