"to project, propel," c. 1300, from Old English þrawan "to twist, turn, writhe, curl," (past tense þreow, past participle þrawen), from Proto-Germanic *threw- (source also of Old Saxon thraian, Middle Dutch dræyen, Dutch draaien, Old High German draen, German drehen "to turn, twist;" not found in Scandinavian or Gothic), from PIE root *tere- (1) "to rub, turn," with derivatives referring to twisting.
Not the usual Old English word for "to throw" (weorpan, related to warp (v.) was common in this sense). The sense evolution may be via the notion of whirling a missile before throwing it. The sense of "put by force" (as in throw in jail) is first recorded 1550s; that of "confuse, flabbergast" is from 1844; that of "lose deliberately" is from 1868. To throw a party was in U.S. college slang by 1916.
To throw the book at (someone) is 1932, from notion of judge sentencing a criminal from a law book full of possible punishments. To throw (one's) hat in the ring "issue a challenge," especially to announce one's candidacy, first recorded 1917. To throw up "vomit" is first recorded 1732. To throw (someone) off "confuse by a false scent" is from 1891.