Why is Saul deposed?

As the text implies, this [erecting a victory stela after a battle] is exactly what Saul thinks he is doing. He has won a glorious victory and taken territory (1 Sam 15:7) and built a monument to himself (1 Sam 15:12), probably crediting Yahweh with the victory. Spoils are taken, not for themselves, as Achan did, but “to sacrifice to the LORD” (1 Sam 15:15). From a typical ancient Near Eastern perspective, Saul has acted with full propriety, as he himself states in 1 Samuel 15:13. However, by sparing the king, Saul has defeated the entire purpose of ḥerem against a community (see proposition eighteen); he may as well have done nothing at all. More severely, however, he has effectively declared independence from his suzerain by honoring himself in place of the emperor and by taking a vassal of his own (Agag’s thinking in 1 Sam 15:32 indicates that he expects to be subjugated rather than executed). This explains Samuel’s odd reference to divination and idols (lit. terāphîm, NIV “idolatry”) in 1 Samuel 15:23; in covenant ideology, these represent breaches of political loyalty to the divine sovereign (see proposition eight). The divine sovereign’s retribution against Saul likewise follows standard procedure; the rebellious regent is dethroned and replaced.— The Lost World of the Israelite Conquest, 227–28