mid-14c., "bishop's tall hat," from Old French mitre and directly from Latin mitra "headband, turban," from Greek mitra "headband, turban," earlier a belt or cloth worn under armor about the waist, perhaps from PIE root *mei- "to bind, attach" (source also of Sanskrit mitra- "friend, friendship," Old Persian Mithra-, god name; Russian mir "world, peace"). The Greek word might be borrowed from Indo-Iranian.
In pre-Christian Latin, in reference to a type of head-dress anciently worn by inhabitants of Lydia, Phrygia, and other parts of Asia Minor, "the wearing of which by men was regarded in Rome as a mark of effeminacy" [OED]. But the word was used in Vulgate to translate Hebrew micnepheth, the sacerdotal head-dress of the ancient Jewish high priests.
c. 1600, "resembling a mitre, of or pertaining to a mitre," from French mitral, from Modern Latin mitralis, from Latin mitra (see mitre). The mitral valve of the heart is so called from 1705, from Modern Latin mitrales valvulae.
in carpentry, "a joint at a 45 degree angle," 1670s, of uncertain origin, perhaps from mitre, via notion of joining of the two peaks of the folded cap. As a verb, to make or join with a miter-joint," from 1731. Related: Mitered. Miter-box is attested from 1670s.
1877, "a Russian commune or village," also (with capital M-) the name of a late 20c. space station, Russian, literally "peace, world," also "village, community," from Old Church Slavonic miru "peace," from Proto-Slavic *miru "commune, joy, peace" ("possibly borrowed from Iranian" [Watkins]), from PIE root *mei- (4) "to bind, tie" (see mitre). Old Church Slavonic miru was "used in Christian terminology as a collective 'community of peace' " [Buck], translating Greek kosmos. Hence, "the known world, mankind."