"God will strike through the head of his enemies" (68:21), and "dipping your foot in blood" (68:23). How can a psalm say that?

First, what the verses say, and who speaks. In 68:21 the psalm speaks about God: "But God will strike through the head of his enemies, the hairy scalp of such a one as still continues in his guiltiness" (68:21). In 68:22-23 it gives words it says the Lord spoke: "The Lord said, “I will bring you again from Bashan, I will bring you again from the depths of the sea" (68:22), "that you may crush them, dipping your foot in blood, that the tongues of your dogs may have their portion from your enemies" (68:23). The psalm names the one struck as "such a one as still continues in his guiltiness" (68:21). It doesn't name the enemies, and it doesn't say who the you of 68:22-23 is. The psalm began with the same enemies: "Let his enemies be scattered! Let them who hate him also flee before him" (68:1). Psalm 68 is not the only psalm with hard words about enemies, and Christians read these words in more than one way. The chapter on Psalm 109 sets out the main readings, each resting on its verses, and chooses none. These notes don't choose either.