c. 1500 shortening of Middle English ampte (late 14c.), from Old English æmette "ant," from West Germanic *emaitjon (source also of Old High German ameiza, German Ameise) from a compound of Germanic *e-, *ai- "off, away" + *mai- "cut," from PIE root *mai- (1) "to cut" (see maim). Thus the insect's name is, etymologically, "the biter-off."
As þycke as ameten crepeþ in an amete hulle [chronicle of Robert of Gloucester, 1297]
Emmet survived into 20c. as an alternative form. By a similar contraction, aunt "a parent's sister" is from Latin amita. White ant "termite" is from 1729. To have ants in one's pants "be nervous and fidgety" is from 1934, made current by a popular song; antsy embodies the same notion.