Middle English mous, from Old English mus "small rodent," also "muscle of the arm" (compare muscle (n.)); from Proto-Germanic *mus (source also of Old Norse, Old Frisian, Middle Dutch, Danish, Swedish mus, Dutch muis, German Maus "mouse").
This is from PIE *mus-, the old Indo-European name of the mouse, retained in several language families (source also of Sanskrit mus "mouse, rat," Old Persian mush "mouse," Old Church Slavonic mysu, Latin mus, Lithuanian muse "mouse," Greek mys "mouse, muscle").
Plural form mice (Old English mys) shows effects of i-mutation. As a type of something timid or weak, from late 14c. Contrasted with man (n.) from 1620s (nor man nor mouse).
The meaning "black eye" (or other discolored lump on the body) is from 1842. The computer sense of "small device moved by the hand over a flat surface to maneuver a cursor or arrow on a display screen" is from 1965, though the word was applied to other things resembling a mouse in shape since 1750, mainly in nautical use.
Parturient montes, nascetur ridiculus mus [Horace]