Mute
Middle English: from Old French muet, diminutive of mu, from Latin mutus .
wiktionary
From Middle English muet, from Anglo-Norman muet, moet, Middle French muet, from mu(“dumb, mute”) + -et, remodelled after Latin mūtus.
From Middle French muetir, probably a shortened form of esmeutir, ultimately from Proto-Germanic.
From Latin mutare(“to change”).
etymonline
mute (adj.)
late 14c., mewet "silent, not speaking," from Old French muet "dumb, mute" (12c.), diminutive of mut, mo, from Latin mutus "silent, speechless, dumb," probably from imitative base *meue- (source also of Sanskrit mukah "dumb," Greek myein "to be shut," of the mouth). Form assimilated in 16c. to Latin mutus. The meaning "incapable of utterance, dumb" is by mid-15c.
mute (v.)
in music, "deaden the sound of," 1861, from mute (n.). Related: Muted; muting.
mute (n.)
late 14c. (late 12c. as a surname), "person who does not speak" (from inability, unwillingness, etc.), from mute (adj.). From 1570s as "stage actor in a dumb show." The musical sense "device to deaden the resonance or tone of an instrument" is by 1811 of stringed instruments, 1841 of horns.