1875, in reference to an awkward sentence, 1892 of a deliberately difficult-to-say phrase, from tongue (n.) + agent noun from twist (v.). The first one called by the name is "Miss Smith's fish-sauce shop."
Old English tunge "tongue, organ of speech; speech, a people's language," from Proto-Germanic *tungō (source also of Old Saxon and Old Norse tunga, Old Frisian tunge, Middle Dutch tonghe, Dutch tong, Old High German zunga, German Zunge, Gothic tuggo), from PIE root *dnghu- "tongue."
For substitution of -o- for -u-, see come. The spelling of the ending of the word apparently is a 14c. attempt to indicate proper pronunciation, but the result is "neither etymological nor phonetic, and is only in a very small degree historical" [OED]. In the "knowledge of a foreign language" sense in the Pentecostal miracle, from 1520s. Tongue-tied is first recorded 1520s. To hold (one's) tongue "refrain from speaking" was in Old English. Johnson has tonguepad "A great talker."
c. 1200 (implied in past tense form twaste), "to wring," from twist (n.). Sense of "to spin two or more strands of yarn into thread" is attested from late 15c. Meaning "to move in a winding fashion" is recorded from 1630s. To twist the lion's tail was U.S. slang (1895) for "to provoke British feeling" (the lion being the symbol of Britain). To twist (someone's) arm in the figurative sense of "pressure (to do something)" is from 1945. Related: Twisted; twisting.
<a href="https://www.etymonline.com/word/tongue-twister">Etymology of tongue-twister by etymonline</a>
Harper, D. (n.d.). Etymology of tongue-twister. Online Etymology Dictionary. Retrieved $(datetime), from https://www.etymonline.com/word/tongue-twister