Green’s Dictionary of Slang

1. to criticize, to reprimand, to attack verbally, to irritate or anger someone.

1951		M. Spillane One Lonely Night 90: You ought to be teeing off on some of the goddam Commies we got loose in this city.
1966		H.S. Thompson Hell’s Angels (1967) 69: Some guys get boozed up and just start teeing off on people.
1970		B. Seale Seize the Time 407: This really teed a lot of us off.
1994		M. Ribowsky Don’t Look Back 300: Larry Doby teed off on him—and teed him off—with two solid base hits.
2021		Betoota-isms 213: So don’t get offended by this chapter if we tee off on your hometown.

2. to hit very hard.

1956		‘Ed Lacy’ Men from the Boys (1967) 57: I teed off on a big kid — and [...] learned I could punch.
1969		J. Crumley One to Count Cadence (1987) 75: The next time you tee off on a guy [...] count me out.
1994		M. Ribowsky Don’t Look Back 300: Larry Doby teed off on him—and teed him off—with two solid base hits.