(a) Does it say somewhere in the Gemara or elsewhere that the Ish iti who took the sair to azazel didn't finish out the year - he always died that year.
(b) If so - why? He was obviously a sheliach mitzvah. Why should his life have been shortened for taking on this assignment?
(a) This is a Midrash cited by the Chizkuni (Vayikra 16:21; the actual location of the Midrash is not clear), as well as the Or ha'Chayim on the verse, the Maharsha here (66b), as well as the Reshash (71a).
(b) The Midrash is not exactly as you expressed it. Rather, the Midrash interprets the words "Ish Iti" to mean "a man whose time has come." This teaches that the Chachamim were supposed to select a person who was destined to die that year to be the Meshale'ach of the Se'ir. Sending away the Se'ir is not the cause of his death. It is the opposite -- since his death is destined to come this year, he was therefore selected as the Meshale'ach. How did they know who would die that year? The Midrash answers that they were well-versed in "Chachmas ha'Mazalos" and therefore they knew who would die (it could have well been a very old man whom they selected).
The reason for this is based on Kabalah, but the gist of it is that we want to satisfy the Accuser on Yom Kipur so that he leaves the rest of us alone. Therefore, we "give" him someone who is anyway destined to die that year, so that he should think that he was victorious in his accusations on Yom Kipur, and thus he will leave everyone else alone.