From Longman Dictionary of Contemporary Englishwork your butt/ass/arse offwork your butt/ass/arse offnot polite to work very hard → work
Examples from the Corpus
work your butt/ass/arse off• In short, I worked my butt off.• I work my butt off for you, while that restaurant is doing worse and worse.• You could have worked your butt off helping a rep and you finally got the rep doing everything right.• I worked my butt off in basketball and stayed on the varsity-in fact, did well.• Meanwhile, Inspiral Carpets went in at grass roots level and worked their butts off in the clubs.• I had to give the ball up, and then I had work my butt off to get it back. 