The unique offering on the Day of Atonement for the sins of Israel consisted of two goats (Leviticus 16:5). The first goat was killed, and the high priest cleansed the sanctuary and the holy objects with its blood. The second goat—the azazel, the goat of departure—had all the sins of the people laid on its head, bearing them to an uninhabited land, a land “cut off.”
Jesus Christ fulfilled the roles of both sacrificial animals: He died to provide a covering of blood and open the way to the Father, and He also bore the sins of many, taking them to the land of forgetfulness—the grave. Isaiah 53 prophesied that the Messiah would accomplish this. Scripture is silent about sins being placed on Satan's head or his bearing sins in any way.
The name of this holy day derives from the Hebrew yom kippur. Kippur means “expiation,” while its root, kaphar, can be translated as “cleanse,” “disannul,” “forgive,” “pardon,” “purge,” “put off,” and “cover.” It is “the Day of Atonement [kippur], to make atonement [kaphar] for you before the LORD your God” (Leviticus 23:28). Leviticus 16:30 summarizes: “For on that day the priest shall make atonement [kaphar] for you, to cleanse you, that you may be clean from all your sins before the LORD.” The holy day deals with providing a solution to the people's defilement—and, therefore, separation from God—through cleansing and removal of sins. As Leviticus 16:21-22 makes plain, the ceremony involves the sins of the people, not of Satan.
The identity of the “goat of departure” has been mired in controversy, yet even without poring over the ritual's details, we can see that the name of the day indicates only one logical way this can take place. The expiation of mankind's sins—the atoning, cleansing, disannulling, purging, and putting away of sins—is what the Savior does, by the very definition of the word, rather than what the Adversary does.
— David C. Grabbe