Or HaChaim on Leviticus 16:10/אור החיים על ויקרא ט״ז:י׳

1 יעמד חי, shall be set alive, etc. These words need analysis. Yuma 40 and Torat Kohanim offer many explanations. According to our own approach the meaning is simply that Aaron was not to confess the sins of Israel on that animal immediately after the lot had been drawn, but was to leave it "alive" for a while. We have explained on several occasions that sinners are called "dead" even while they are physically still alive. An animal which carries the burden of the sins of the nation would therefore certainly be considered "dead" from the moment it assumed that burden. Consequently, the Torah had to mention that this procedure was not to take place immediately and that in the meantime the scape-goat remained "alive." Our interpretation is confirmed by the Torah as correct as you can see from verse 21. Only then does Aaron place his hands (weight) on the head of the שעיר החי, the "living goat," and confesses the sins of the people and transfers them to the head of that animal. At that point the Torah no longer adds the adjective "the live one," when speaking of the scapegoat. Seeing the animal is considered dead from that point on we can understand why the messenger who took the scapegoat to the place from where it was thrown off the rock had to immerse himself in a ritual bath. He had become ritually defiled by contact with an animal considered dead according to halachah though it had been walking all the time that the איש עתי accompanied it (verse 22).