send-off n.

Middle English senden, from Old English sendan "dispatch (as a messenger, on an errand); order or cause to go or pass (from one place to another);" also "send forth, emit; throw, propel, cause to be delivered or conveyed."

This is reconstructed to be from Proto-Germanic *sond- "make to go" (source also of Old Saxon sendian, Old Norse senda, Old Frisian senda, Middle Low German and Middle Dutch senden, Dutch zenden, German senden, Gothic sandjan), causative form of *sinþan "to go, journey" (source of Old English sið "way, journey," Old Norse sinn, Gothic sinþs "going, walk, time"). This in turn is from the PIE root *sent- "to head for, go" (source also of Lithuanian siųsti "send"), for which see sense (n.). For the linguistic connection of "go" and "sense," compare German sinnen (past tense sann) "go over in the mind, review, reflect upon." 

The meaning cause (someone) to go into some specified state (send to sleep, etc.) is by 1831. The slang sense of "to transport with emotion, delight" is by 1932, in American English jazz slang. To send word "transmit or dispatch a message" (to someone) is from c. 1200. To send for "summon, send a message or messenger for" is by late 14c.

by c. 1200 as an emphatic form of Old English of (see of), employed in the adverbial use of that word. The prepositional meaning "away from" and the adjectival sense of "farther" were not firmly fixed in this variant until 17c., but once they were they left the original of with the transferred and weakened senses of the word. Meaning "not working" is from 1861.

Off the cuff "extemporaneously, without preparation" (1938) is from the notion of speaking from notes written in haste on one's shirt cuffs. In reference to clothing, off the rack (adj.) "not tailored, not made to individual requirements, ready-made" is by 1963, on the notion of buying it from the rack of a clothing store; off the record "not to be publicly disclosed" is from 1933; off the wall "crazy" is 1968, probably from the notion of a lunatic "bouncing off the walls" or else in reference to carom shots in squash, handball, etc.