chop: There are three distinct words chop in English. The oldest  originally meant ‘trade, barter’, but it is now found only in the phrase chop and change. It appears to come from Old English cēapian ‘trade’, which is related to English cheap. Chop ‘jaw, jowl’  (now usually in the plural form chops) is of unknown origin; the now archaic chap is a variant. Chop ‘cut’  seems ultimately to be the same word as chap (as in ‘chapped lips’), and may be related to Middle Low German kappen ‘chop off’. The specific noun sense ‘meat cutlet’ dates from the 15th century. => chap, cheap
"to cut with a quick blow," mid-14c., of uncertain origin, perhaps from Old North French choper (Old French coper "to cut, cut off," 12c., Modern French couper), from Vulgar Latin *cuppare "to behead," from a root meaning "head," but influenced in Old French by couper "to strike." Related: Chopped; chopping.
"shift quickly," 1530s, earlier "to bargain" (early 15c.), ultimately from Old English ceapian "to bargain" (see cheap); here with a sense of "changing back and forth," probably from common expressions such as to chop and change "barter." To chop logic is recorded from 1570s. Related: Chopped; chopping.