Normally, when we think of a scapegoat, we think of an innocent person who is being blamed and punished in lieu of the actual guilty parties. However, it appears that the actual meaning of the ritual involving the scapegoat on the Day of Atonement (also known as Yom Kipur) is intended to convey a story with a very different meaning.
The word translated "scapegoat" in Leviticus 16:8 is "Azazel" ("עזאזל").
One root here is "ʕ-z-l" having the meaning "remove" and the additional az- at the beginning is often described as a reduplicative intensifier.
Rabbi Rashi described Azazel's meaning saying, the word is taken to be a compound of עזז "to be strong" and אל "mighty".
In the Yom Kipur tradition of the scapegoat, two goats would would be brought to a priest who would cast lots to determine the goats' fates. On one goat would fall the lot of the Lord, and on the other would fall the lot of Azazel. The goat on whom, the lot of the Lord fell would be sacrificed, and the goat on whom the lot of Azazel fell would be chased out of town, out through the Kedron Valley, about 6 or more miles.
Ibn Ezra asserted that Azazel was the name of a mountain, perhaps close to Mount Sinai, where the sin offering goat was originally chased until he slipped off a high place, fell down the mountain, and died. In more recent tradition, the scapegoat was chased out to a ravine and then pushed in.
It is worthwhile to highlight that according to our record regarding the Jewish tradition, the two goat were supposed to be, for all intents and purposes, identical. To me this echoes traditions that portray both Satan, and Jesus, somewhat identically, as serpents.
It appears that the story of the scapegoat is intended to be the story of a wicked figure, cast out and destroyed, perhaps, even in a very you-created-your-own-fate kind of way. At the very least, this is how it is often treated in Jewish tradition. However, an alternate interpretations see the goat as either an offering to a desert demon, a payment to a desert demon, or as a means of conveying the sins of the people out to this demon.
The Book of Enoch records "Azazel" as the name of a fallen angel who the Lord commands to be punished by casting him into a rift in the Earth and then buried with rough rocks. As he is noted to have taught the children of men various arts which caused them to sin against each other, the Lord commands to ascribe all sin to him. In this way, the goat on which the lot of the Lord fell, which is killed, can be seen as representing the Lord, and the lot upon which the lot fell for Azazel can be seen as representing this evil entity which taught men to sin.
The story of Azazel in the Book of Enoch incorporates both the idea of removing and the idea of being strong and mighty.
It is interesting to note that Satan, Cain, and Korihor all have stories that share in this scapegoat story structure. Interestingly, though, Nephi seems to be making direct analogy between himself and the scapegoat in the story of his slaying of Laban, even though it is Laban who is the antagonist in that story. (See: 1 Nephi 3:31-4:38)
Jesus Christ is particularly interesting in this regard, because tellings of his story appear to incorporate ideas from both of the goats of Yom Kipur. In having the Jewish people choose between Jesus and Barabas (son of the father), we have a situation set up that is very similar to the choosing of the scapegoat for yom-kippur. The people choose Barabas "son of the father" to set free, symbolically then, Jesus is chosen by the people for the lot of Adonai, and he is killed. On the other hand, it is worth considering that the scapegoat was sent out of Jerusalem and killed too. The purpose for this is sometimes described as being to prevent the goat, laden with the sins of the people, from bringing those sins back into the city. Similarly, on two different occasions during the atonement, Jesus makes a trek outside the city walls carrying a burden. The first time is directly after the last supper, when he travels across the Kedron valley, much like the scapegoat does, and then ascends the mount of olives, carrying the burden of our sins, and then atones for those sins. The second time, is after he is condemned to die, and he carries the cross out to Golgotha to be crucified and then buried in a tomb of stone. It is curious that he can fulfill both roles simultaneously.
One explanation for how he can, as a righteous man, fulfill the role of the goat of Azazel (similar to Nephi), is that the role of the goat is not to BE Azazel, but to carry away our sins TO Azazel, who some interpret to be a desert demon, but who we would take to be our accuser, Satan. This feels contrary to the spirit of the Book of Enoch, but that may not be a very serious shortcoming. In this case, the goats then have to be identical, because they are, in fact, the same, in a sense. (Though we still have the Barabas acting as a scapegoat figure, and I would not be surprised if other similar figures are later identified considering how this act seems to play out multiple times.)
The Book of Omni identifies yet another "mighty and strong" figure who led a group toward the land of Nephi. He dies (though this isn't made completely clear in Omni) along with many others he lead. The reference to this man being mighty and strong, I would think, is intended to connect the negative imagery of Azazel to the character.