A common view of the azazel goat—sometimes translated as "scapegoat"—is that it represents Satan, on whose head the sins of humanity will be placed. However, the source of this interpretation is the apocryphal Book of Enoch.
In the Book of Enoch, “Azazel” is the name of a demon blamed for all the sins of mankind (Enoch 10:8). He is not the chief demon—not actually Satan (Enoch 6:3; 9:7). Azazel is bound and cast into darkness, confined to the desert until the day of judgment:
And again the Lord said to Raphael: 'Bind Azâzêl hand and foot, and cast him into the darkness: and make an opening in the desert, which is in Dûdâêl, and cast him therein. And place upon him rough and jagged rocks, and cover him with darkness, and let him abide there forever, and cover his face that he may not see light. And on the day of the great judgment he shall be cast into the fire. (Enoch 10:4-6)
Bizarrely, all of humanity's sins are ascribed to this demon, not to the chief demon, yet in Leviticus 16, the sins are allegedly placed on Satan's head. If this demon is the fountainhead of mankind's sins, why is Satan held responsible? Even so, this is the clever counterfeit that links the Hebrew word azazel with something evil. Without the Book of Enoch, nothing ties Leviticus 16 to the binding of Satan.
Notice the contrast between what happens to the biblical azazel (“goat of departure” or "complete removal") and what befalls Satan. God's purpose for the azazel goat is to “bear on itself all their iniquities to an uninhabited land.” His purpose for Satan's binding is “so that he should deceive the nations no more till the thousand years were finished.” These purposes are also completely dissimilar.
Satan's binding effectively and thoroughly stops his work as the “prince of the power of the air” (Ephesians 2:2). While the pit facilitates temporary protection from his influence, God will release Satan to deceive again (Revelation 20:7-8). Satan remains unrepentant and continues his evil work. His binding provides a reprieve but no atonement.
In contrast, the live goat acts as a substitutionary sacrifice, and by itself, this nullifies the possibility of it representing either Satan or another demon. The goat's role was to bear iniquities. In the ritual, the sins were those of the children of Israel. Scripture provides multiple witnesses that Jesus Christ bears mankind's sins (Isaiah 53:11-12; I Peter 2:24; Hebrews 9:28) and that God would lay the iniquity of us all on the Messiah (Isaiah 53:6).
Conversely, neither Satan's nor a demon's sins are in view in Leviticus 16. An unblemished animal—symbolizing sinlessness—could in no way represent either of them, and for the same reason, neither qualifies to be a substitutionary sacrifice. In addition, there is no biblical basis for placing humanity's sins on Satan's or a demon's head.
Revelation 20:1-3 makes no mention of atonement, justification, reconciliation, cleansing, propitiation, human sin, or any other theme found in Leviticus 16. Instead, Satan is bound to curtail his influence on the nations, not to satisfy God's justice. Scripture provides no legal foundation for his binding to pay the debt for sin, whether his own or mankind's. The wages of sin is death, and the gift of God is eternal life in Jesus Christ (Romans 6:23), but the confinement of Satan neither pays those wages nor facilitates that gift.