Two Labour councillors complained after Nick Martin made the comments last year
Swindon's mayor has resigned after making derogatory remarks about disabled people during a meeting.
Conservative Nick Martin, 63, was found guilty of breaching the members' code of conduct after Labour complained about comments he made last year.
Labour councillors said they heard him say: "Are we still letting Mongols have sex with each other?"
The standards committee ruled he must apologise but Mr Martin said it was a word he "was brought up with".
In a letter to the council, Mr Martin said it was "with regret" that he submitted his resignation as mayor "with immediate effect".
He added that, following the accusations against him, he had cooperated with the independent standards investigation.
"I have made new apologies and am abiding by the other recommendations from the Standards Assessment Panel," he said.
"However, it is clear that this will not stop the attacks on the office and person of mayor."
Mr Martin was reported to the standards committee by Labour councillors Ray Ballman and Junab Ali after the remarks were made at a Swindon Borough Council meeting last year.
Last Thursday, the committee ruled Mr Martin must make a public apology within seven days and attend further training within a fortnight.
Conservative leader of the council, David Renard, said the process had "proved to be a robust system".
"It was right and proper that due process took its course," he said.
"The mayor accepted the recommendations and has agreed to resign. I think he has made the best decision that he could, in the interests of the office of the mayor and all involved."