Saul did not kill all the Amalekites seeing as they continued to be a threat to Israel even after their defeat (see 1 Samuel 27:8; 1 Samuel 30:1; 2 Samuel 8:12; Psalm 83:2–7; Esther 3:1, Esther 3:10). The description is possibly emphasizing a complete but not a final victory.1 Alternatively, with the Amalekites being semi-nomadic, it is possible that some of them were absent from the region when Saul conducted his campaign, and that these were the group who later attacked David (1 Samuel 30:1).
8 And he took Agag the king of the Amalekites alive and devoted to destruction all the people with the edge of the sword.