word-forming element typically representing cross as a noun, adverb (cross-examine), adjective (crossbar), and in many words a confluence of them. "There is no distinct line of division between cross as an adjective and cross as a prefix. As a prefix, it often represents the adv. cross, or the prep. cross, across." [Century Dictionary]
Old English stice "a prick, puncture, sting, stab," from Proto-Germanic *stikiz (source also of Old Frisian steke, Old High German stih, German Stich "a pricking, prick, sting, stab"), from PIE *stig-i-, from root *steig- "to stick; pointed" (see stick (v.)). The sense of "sudden, stabbing pain in the side" was in late Old English.
Senses in sewing and shoemaking first recorded late 13c.; meaning "bit of clothing one is (or isn't) wearing" is from c. 1500. Meaning "a stroke of work" (of any kind) is attested from 1580s. Surgical sense first recorded 1520s. Sense of "amusing person or thing" is 1968, from notion of laughing so much one gets stitches of pain (compare verbal expression to have (someone) in stitches, 1935).
<a href="https://www.etymonline.com/word/cross-stitch">Etymology of cross-stitch by etymonline</a>
Harper, D. (n.d.). Etymology of cross-stitch. Online Etymology Dictionary. Retrieved $(datetime), from https://www.etymonline.com/word/cross-stitch