The 45-year-old caused a frenzy on social media, as he ate the pie on the substitutes’ bench during the game at Gander Green Lane.
The Gambling Commission later announced they would investigate the incident, after Shaw admitted he was aware Sun Bets offered odds of 8-1 that he would eat a pie “live on air.”
Sutton manager Paul Doswell has now confirmed the keeper has offered to cancel his contract.
“It’s been very disappointing, no doubt about that,” he told Sky News.
“I woke up this morning to this storm of criticism and it’s something we have dealt with quickly as a club.
“Wayne has offered his resignation to the chairman this afternoon and its been accepted. It’s a very, very sad end to what’s been a great story.”