Green’s Dictionary of Slang

punt v.2

[US football imagery; the team that fails to score within four downs is forced to punt the ball to the opposition]

1. (US campus) to give up, esp. one’s work.

[US]Baker et al. CUSS 178: Punt Waste time, not study. Do poorly on an exam.
[US]G. Underwood ‘Razorback Sl.’ in AS L:1/2 64: I’m going to have to punt in chemistry.
[US]J. Doyle College Sl. Dict. 🌐 punt [MIT] to cut class, skip a problem set, or otherwise avoid doing academic work.

2. to dismiss from a job.

[Scot]T. Black Artefacts of the Dead [ebook] Bob, get real, if the Sun punts Sinclair he’ll just go freelance and chase us but with an axe to grind this time.
[Aus]N. Cummins Adventures of the Honey Badger [ebook] VITAL AUSSIE VERNACULAR Get the Arse: Get sacked or punted.

In phrases

punt off (v.)

(US campus) to forget, to put to the back of one’s mind.

[US]G. Underwood ‘Razorback Sl.’ in AS L:1/2 64: Why don’t you just punt the whole thing off?