Apocopate \uh-POK-uh-peyt\ , verb;
1. To omit the final sound or sounds of (a word).
Hmm, this word is suspiciously linguistic-sounding. I'm assuming this means saying things like 'tellin' without pronouncing the full \ŋ\ (which is -ng, for those unfamiliar with the phonetic alphabet). 'Gonna' is similar because 'going' loses the full \ɪŋ\ (-ing) sound, but since it's elided with 'to' it's not simply apocopated.
This word does not exits in Etymonline.com, and the Oxford English dictionary doesn't have much on the verb apocopate. The participle adjective entry refers to apocope, which means "The cutting off or omission of the last letter or syllable of a word," so this is obviously from where today's word is derived. Apocope comes from Greek words meaning "a cutting off" or "to cut off".
*Today's word and the first definition were both taken from Dictionary.com's 'Word of the Day' for Wednesday, October 13