You run your ass off.
Can ass be the object of run? Why isn’t it just “you run”?
You run your ass off
implies that you are running so hard that your buttocks fall off. Obviously that never happens, but it is a figurative way of stating that you are doing something to the point of exhaustion and beyond. It is a familiar trope used with other pursuits as well:
I worked my ass off on that project.
We’re going to party our asses off once we graduate.
And so on.