Why is a goat thrown off of Azazel on Yom Kippur to atone for Klal Yisroel’s sins?
I.e., why does the Torah deviate from the usual manner of sacrifice via Sh’chita and instead have the messenger cast the goat off a cliff?
I understand that animal is torn to pieces even before it reaches half way down so it’s not a prolonged death but what is the purpose of achieving the kaparah in this fashion?
You are asking a good question. It is written in Pirkei D’eliezer (one of the Tanaim) that the reason for the Azazel was to be a sort of sacrifice or present to the satan. Yom Kippur is a day of judgment, and the Satan comes to testify against the Jews, and to prosecute them. The Azazel is meant as a form of a present to pacify him. It is not meant to be a regular sacrifice, because it is not going to G-d, and it, is in a way, a form of letting it out. There is also a hidden lesson here, since the Azazel in a way carries the sins of the Jews, it’s terrible end has a deep message, that one person who sins will have to pay a heavy price, and this is meant to encourage us to rectify our ways.