Albert Barnes Commentary Psalms 18:40

"Thou hast also made mine enemies turn their backs unto me, That I might cut off them that hate me." — Psalms 18:40 (ASV)

You have also given me the necks of my enemies - Their necks to tread upon, as the result of victory, or their necks to be subject to me, as the neck of the ox is to its owner. The phrase is sometimes used in this latter sense to denote subjection ; but it is more commonly, when applied to war, used in the former sense, as denoting complete triumph or conquest. It was not uncommon to trample on the necks of those who were overcome in battle (Ezekiel 21:2; Genesis 49:8). The word used here - ערף ‛ ôreph - properly means neck, nape, or the back of the neck; therefore, 'to give the neck' sometimes means to turn the back, as in flight, and the phrase could admit that meaning here.

So Gesenius (Lexicon) understands it. So also DeWette: “You turn my enemies to flight.” It seems to me, however, that the more probable interpretation is that of complete subjection - as when the conqueror places his foot on the necks of his foes. This is confirmed by the next member of the sentence, where the psalmist speaks of the complete destruction of those who hated him.

That I might destroy them that hate me - That have pursued and persecuted me in this manner. The idea is that of utterly overcoming them, of putting an end to their power, and to their ability to injure him.