“to sacrifice.” This was likely a lie. God’s “sacrifice” was to destroy the animals. There is no reason to assume that Yahweh would have been happier with one type of sacrifice than the sacrifice of devoting the animals to destruction. It seems that Saul invented this to save face.
“to Yahweh your God.” It is interesting in this record in 1 Samuel 15 that Saul repeats the phrase “Yahweh your God” (meaning Yahweh, Samuel’s God) three times in this chapter (1 Sam. 15:15, 21, 30). Saul never just says, “to Yahweh,” or “to Yahweh our God,” but always, “to Yahweh your God.” It is unclear exactly why Saul did that, but it seems like he is somehow distancing himself from Yahweh, as if to say, “Yahweh and His commands are between Yahweh and you, while I am king over the people and must take care of them.” In any case, it is clear that since Saul made the statement three times in the conversation that he was distancing himself from Yahweh and his responsibility to do exactly what Yahweh commanded.
“devoted...to destruction.” That is, destroyed them all. [For more on things “devoted” to Yahweh and devoted to destruction, see commentary on Josh. 6:17].