“Agag the king of the Amalekites.” Saul did not kill all the Amalekites and not even all the descendants of Agag, as we see from the Book of Esther (see commentary on Esther 3:1).
“devoted to destruction.” Saul and his army killed all the people. [For more on things “devoted” to Yahweh and devoted to destruction, see commentary on Josh. 6:17].
“the mouth of the sword.” Used to show great destruction, as if the sword was eating its victims (see commentary on Josh. 6:21).