The divine destroying angel is the Josephite, whose angelic name we don't know, but I will assume it is Gazelem. Gazelem appears to be separate from all the other angels, reporting to no one but God Himself and appears to be the personal servant or valet of the Lord. His ministry is one of justice and judgment.
Whenever God needs to send down a message, He sends one of the innumerable angelic hosts, as messengers, but whenever He wants to send down destruction, He sends Gazelem.
Gazelem is the one who destroyed the whole world in the Flood of Noah, irrespective of anyone's age. Even innocent infants, animals and plants were killed. A normal angel would not want to do that, but Gazelem had no qualms about it. Some think that the planet Jehovah (a brown dwarf) passed by, causing the flood, but that view is incorrect. It wasn't Jehovah's throne (the brown dwarf) that passed by, but Gazelem's throne (a giant, planet-size comet), which is called by the Lord, the destroyer:
(D&C 105:15)Behold, the destroyer I have sent forth to destroy and lay waste mine enemies; and not many years hence they shall not be left to pollute mine heritage, and to blaspheme my name upon the lands which I have consecrated for the gathering together of my saints.
Gazelem is the one who killed all those Egyptian first-born children. Gazelem is the one God sent down to save Abraham from the priest of Pharaoh by destroying the altar of Elkenah and all the idol gods and killing the priest. Gazelem, though, was not the one sent to Sodom and Gomorrah. Instead, three angels were sent and they ended up sparing some people, including Zoar:
(JST Gen. 19:30-32)And the Lord did not destroy Sodom until Lot had entered into Zoar. And then, when Lot had entered into Zoar, the Lord rained upon Sodom, and upon Gomorrah; for the angels called upon the name of the Lord for brimstone and fire from the Lord out of heaven. And thus they overthrew those cities and all the plain, and all the inhabitants of the cities, and that which grew upon the ground.
Had Gazelem been sent, Lot would have been destroyed along with everyone else. Gazelem, then, is not concerned with mercy and compassion, but with justice and judgment. He is referenced throughout the scriptures, being called the destroying angel, or just the destroyer:
(D&C 89:21)And I, the Lord, give unto them a promise, that the destroying angel shall pass by them, as the children of Israel, and not slay them. Amen.
(Exodus 12:23)For the Lord will pass through to smite the Egyptians; and when he seeth the blood upon the lintel, and on the two side posts, the Lord will pass over the door, and will not suffer the destroyer to come in unto your houses to smite you.
The demonic destroying angel
When Lucifer rebelled in heaven, and persuaded one-third of the heavenly hosts to rebel with him, and commit spiritual suicide, it appears that he patterned himself after Gazelem.
Gazelem is God's mighty and strong one, who doesn't need anyone's help to do anything. He can kill his own snakes, no matter how big, no matter how many. He can do an infinite number of impossible things, without needing the help of any other angels.
(Isaiah 28:2)Behold, the Lord hath a mighty and strong one, which as a tempest of hail and a destroying storm, as a flood of mighty waters overflowing, shall cast down to the earth with the hand.
Gazelem can destroy anything, including souls. Guess who will be the one who "hews the wicked souls down and casts then into the lake of fire and brimstone?" Gazelem, then, is God's destroyer of souls.
Now, Lucifer doesn't give a hoot about mercy or compassion, very much like Gazelem. Lucifer desired to be just as strong and powerful as Gazelem, and sought such power by getting fully one-third of the hosts of heaven behind him. With such a force behind him, no single angel can take Lucifer on. This is why Michael needed the rest of the angelic armies (the two-third) to cast out Satan and his angels from heaven. However, Gazelem alone could have done it. Why didn't he do it? One of the reasons is because Gazelem would not have cast out Satan and the one-third. Instead, he would have destroyed them. They were cast out to earth to tempt man, to further the purposes of the Lord, therefore, they weren't, yet, to be destroyed. So, Gazelem sat that one out.
Satan's plan, then, is to get mankind to sin, knowing that God has a divine destroying angel at hand, who will destroy every single soul that sins. Satan destroys souls in this way, becoming himself a demonic destroying angel, using Gazelem's destroying nature to kill the creations of God.
The two angels, then, are like two sides of the same coin. Both are all about judgment and justice and no mercy, no compassion. Both are all about destroying souls. Both operate independently from any angelic hierarchy. Gazelem reports to God alone, Satan reports to no one, becoming the god of this earth. But one is more powerful than the other.
How, then, does God deal with Satan? By siccing Gazelem on him.
(Psalms 110:2)The Lord said unto my Lord, Sit thou at my right hand, until I make thine enemies thy footstool. The Lord shall send the rod of thy strength out of Zion: rule thou in the midst of thine enemies.
Gazelem, the rod of God's power, then, is sent down to earth, in the last days, near the end times, and is born of a woman, and this Gazelem will act just like he always acted, destroying everything around him that he sees is wicked or unfit for the coming King, whether of man or beast, making all of God's enemies His footstool.
At some point Gazelem gets fully unleashed, and one of his last acts is to lay his embodied hand upon the spirit body of Satan (an impossible thing to do) and bind him and his angels for a thousand years with a chain:
(Revelation 20:1-3)And I saw an angel come down from heaven, having the key of the bottomless pit and a great chain in his hand. And he laid hold on the dragon, that old serpent, which is the Devil, and Satan, and bound him a thousand years, and cast him into the bottomless pit, and shut him up, and set a seal upon him, that he should deceive the nations no more, till the thousand years should be fulfilled: and after that he must be loosed a little season.
How does one chain up a spirit, or one-third of the former spirits of heaven (for they all come with Satan), who are essentially infinite in number? Is the chain spiritual, or physical? The whole thing is impossible, but Gazelem does it anyway.
We now have to deal with two destroyers
For sixth thousand years, mankind has had to deal solely with the demonic destroying angel: Satan. But now this Gazelem fellow is on earth, and is about to stand up, and this guy is a thousand times more deadly and terrifying than the other guy. Nobody ought to make the mistake that we are going to see another merciful, Christlike figure stand up. Gazelem/Joseph-Nephi has an altogether different nature than Christ. He's more like God the Father, manifesting the divine justice of God, than like the merciful Christ.
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