late 14c., "to remove the skin from" (originally of circumcision), from skin (n.). As "to have (a particular kind of) skin" from c. 1400. In 19c. U.S. colloquial use, "to strip, fleece, plunder;" hence skin-game, one in which one player has no chance against the others (as with a stacked deck), the type of con game played in a skin-house. Skin the cat in gymnastics is from 1845. Related: Skinned; skinning.
Others are reading
<a href="https://www.etymonline.com/word/skint">Etymology of skint by etymonline</a>
Harper, D. (n.d.). Etymology of skint. Online Etymology Dictionary. Retrieved $(datetime), from https://www.etymonline.com/word/skint