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Old English cropp "bird's craw," also "head or top of a sprout or herb." The common notion is "protuberance." Cognate with Old High German kropf, Old Norse kroppr. Meaning "harvest product" is c.1300, probably through the verbal meaning "cut off the top of a plant" (c.1200).
"cut off the top of a plant," c.1200, from crop (n.). The general meaning of "to cut off" is mid-15c. Related: Cropped; cropping. Women's fashion crop top is attested from 1984.