So David here is asking God to bring such people down—take away their power and even their lives if need be—for their sins, which is part of the curse of the law. They already carried the death penalty. David is just asking for it to be enacted. Their actions, which are clearly unrepented of, deserved the worst of punishments. And David requests God to fight for him. He asks for deliverance, and he asks for it that they may know that this is Your hand—that You, Lord, have done it.
He does not want to be part of the curse; he does not want to give them the violence that he is asking for; he wants God to do that. What does God say? It is mentioned in both testaments: "Vengeance is Mine; I will repay." And he is just basically saying, "God, please take that vengeance. I don't want to be part of it, but You know the best way to do this." So he is putting dealing with his enemies in God's hands, not his own, because he knows God will deal with them righteously and give them what they deserve. David here asks only for justice and equity.
