"offspring of donkey and horse," from Old English mul, Old French mul "mule, hinny" (12c., fem. mule), both from Latin mulus (fem. mula) "a mule," probably from a pre-Latin Mediterranean language.
Properly, the offspring of a he-ass and a mare; that of a she-ass and a stallion is technically a hinny. Used allusively of hybrids and things of mixed nature. As a type of spinning machine, attested from 1797 (so called because a hybrid of distinct warp and woof machines). Meaning "obstinate, stupid, or stubborn person" is from 1470s; that of "narcotics smuggler or courier" first attested 1935.