The Lord promised to hand over the men to Israel slain
and all that Joshua had to do was hamstring the horses and burn the chariots. This suggests that the Lord killed them, perhaps in a similar manner to what we read in 2 Kings 19:35.1 There the angel of the Lord struck down all the Assyrian solders of King Sennacherib in one night.
However, we do also read that Israel attacked the armies of these northern kings and chased them to Misrephoth Maim (West) and the Valley of Mizpah (East). This suggests that Israel had a role to play in the destruction of the army, albeit a small one. There are not impressive miracles recorded; we are simply told that the Lord fought for Israel and handed their enemies over to them.2
6 And the LORD said to Joshua, “Do not be afraid of them, for tomorrow at this time I will give over all of them, slain, to Israel. You shall hamstring their horses and burn their chariots with fire.”