Is there a word for the discarded part of a word that is truncated?
There is not a single word for that, the usual term is:
elided part/ portion
Those would be "elisions".
From WordNet (r) 3.0 (2006) [wn]:
elision n 1: omission of a sound between two words (usually a vowel and the end of one word or the beginning of the next) 2: a deliberate act of omission; "with the exception of the children, everyone was told the news" [syn: {exception}, {exclusion}, {elision}]