in golf, 1721, back-formation from teaz (1673), taken as a plural; a Scottish word of uncertain origin. The original form was a little heap of sand. The verb meaning "place a ball on a golf tee" is recorded from 1673; figurative sense of "to make ready" (usually with up) is recorded from 1938. Teed off in the figurative sense of "angry, annoyed" is first recorded 1953, probably as a euphemism for p(iss)ed off.
To hit someone or something very hard: He hit a homer, really teed off
[1953+; fr the opening shot of each hole in golf, off the tee]