"Therefore thus says the Lord God of hosts: O my people, who live in Zion, do not be afraid of the Assyrians when they beat you with a rod and lift up their staff against you as the Egyptians did. For in a very little while my indignation will come to an end, and my anger will be directed to their destruction. The Lord of hosts will wield a whip against them, as when he struck Midian at the rock of Oreb; his staff will be over the sea, and he will lift it as he did in Egypt. On that day his burden will be removed from your shoulder, and his yoke will be destroyed from your neck" (Isaiah 10:24-27).
I've added the three verses that precede 10:27, which is the verse you are asking about. On its own it would be difficult to know who the 'he' is whose burden and yoke will be rmoved. In context it is clearly the Assyrian nation that is being described. The prophet is assuring the people, on behalf of the Lord God, that the oppression they are enduring will come to an end—evoking the story of the deliverance from Egypt as a point of reference.
It might seem that the Lord is being very unpredictable, shifting his consequences from the Israelites to the Assyrians. In Truth, however, we understand that both sets of consequences are the result of mortal choices. The nation of Israel has placed other priorities ahead of its covenant with the Divine, and the consequence is captivity. The Assyrians are proving to be equally arrogant, and their inevitable consequences are forthcoming.
It's no less true for us today that choices have consequences. There is no judgment involved; it's simply the outpicturing of divine law. If we are experiencing negative energies in our lives, their source can be found in the choices we've made.