c.1300, from a Scandinavian source such as Old Norse myrr "bog, swamp," from Proto-Germanic *miuzja- (source of Old English mos "bog, marsh"), from PIE *meus- "damp" (see moss).

c.1400, in figurative sense of "to involve in difficulties," from mire, n.. Literal sense is from 1550s. Related: Mired; miring.