Albert Barnes Commentary Psalms 109:15

"Let them be before Jehovah continually, That he may cut off the memory of them from the earth;" — Psalms 109:15 (ASV)

Let them be before the Lord continually - Let their sins never pass from the mind of God. Let Him never forget them to the extent that He refrains from inflicting punishment for them.

That He may cut off the memory of them from the earth - That they may be wholly forgotten among people. Let their very name perish; and let the offender in this case be in the condition of those who have no ancestors to whom they can refer with pride and pleasure. The idea here is drawn from the honor which is felt in being able to refer to ancestors worthy of being remembered for their virtues.