"decoration of a surface with an applied paper cut-out," by 1957, from French découpage, literally "the act of cutting out," from decouper "to cut out" (12c., Old French decoper), from dé- "out" (see de-) + couper "to cut" (see chop (v.1)).
active word-forming element in English and in many verbs inherited from French and Latin, from Latin de "down, down from, from, off; concerning" (see de), also used as a prefix in Latin, usually meaning "down, off, away, from among, down from," but also "down to the bottom, totally" hence "completely" (intensive or completive), which is its sense in many English words.
As a Latin prefix it also had the function of undoing or reversing a verb's action, and hence it came to be used as a pure privative — "not, do the opposite of, undo" — which is its primary function as a living prefix in English, as in defrost (1895), defuse (1943), de-escalate (1964), etc. In some cases, a reduced form of dis-.
"to cut with a quick blow," mid-14c., of uncertain origin, not found in Old English, 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" (see coup). There are similar words in continental Germanic (Dutch, German kappen "to chop, cut").
Related: Chopped; chopping. Chopping-block "block of wood on which anything (especially food) is laid to be chopped" is from 1703.
<a href="https://www.etymonline.com/word/decoupage">Etymology of decoupage by etymonline</a>
Harper, D. (n.d.). Etymology of decoupage. Online Etymology Dictionary. Retrieved $(datetime), from https://www.etymonline.com/word/decoupage