Bite/chew your arm off

To bite or chew your arm off for something means that one would go to any lengths to achieve a desired objective even at the cost of your arm. The expression is originally American from the latter half of the 20th century, but has now spread across the English-speaking world. It is not known who actually coined the expression but it supposedly derives from hunting and trapping. Trappers would often find an animal’s paw in their traps, chewed off so that the animal could escape. That is why the expression, somewhat bizarrely, is linked to the expression 'coyote ugly' in the sense that after a drunken one-night stand, if one woke up with a very ugly person asleep on one’s arm, one would rather bite or chew it off rather than wake them.