Biagini, who has taught art at a high school in Pittsburgh, Pennsylvania, for 14 years, entered the contest on DJ Bubba the Love Sponge's show on the Sirius station.
The prize was a filmed date with Asa Akira, the star of Bombshell Bottoms 4 and Top Notch Bitches 7, in Florida.
Mr Biagini said the date was staged and he had entered because he wanted to visit the town of St Petersburg, home to a Salvador Dali museum.
The teacher, who uses a wheelchair, also claimed he had been ridiculed on the show over his disability, which the station denied, saying he had been aware of the contest's nature when he entered.
The school board voted to accept Mr Biagini's offer to resign after news of the contest was broadcast.