turn not away the face of thine anointed - that is, of me, who by Thy promise and appointment have been installed as king and ruler of Israel. The words are equivalent in meaning to this: Do not reject my present petitions; do not send me from Thy throne of grace dejected in countenance and disappointed in heart.
remember the mercies of David thy servant - that is, the mercies promised to David, and in consideration of that promise, hear and answer my prayer (compare Psa 132:10).