The ax, saw, rod, and staff are metaphors referring to the Lord’s cutting Israel down, with Assyria serving as the tool he used. Regarding proud boasting, the Lord has said, “In nothing doth man offend God, or against none is his wrath kindled, save those who confess not his hand in all things, and obey not his commandments” (D&C 59:21).
“His fat ones” refers to the soldiers of the Assyrian king. “Under his glory” refers to the “glory” of the Assyrian. Kindling a “burning like the burning of a fire” could refer to, at least in part, the feverish plague in the Assyrian camp in the fateful year 701 b.c., when the Lord began to cut down the mighty empire.