ציטירנדיקער פּירוש אויף שמואל א 15:3

And he commands commandments and [enacts] prohibitions about a matter that is not from the Torah – for example, he says, "Fight against city x" or "nation y, now"; as Shmuel commanded Shaul to fight against Amalek (I Samuel 15).

מחוטב עציך עד שואב מימיך, from the leader of the wood choppers to the most lowly of the water carriers. The construction here parallels comparisons as מעולל ועד יונק, “infants as well as sucklings,” (Samuel I 15,3) i.e. the highest ranking within its category to the lowliest ranking. Similar expressions are used when the Torah speaks of משור ועד שה, oxen as well as lambs, meaning the most expensive animals of your livestock to the least expensive. Similarly,מגמל ועד חמור, “from the camels down to the donkeys.”

מחה אמחה את זכר עמלק, not only the people but even their livestock. We know this from the instructions given by the prophet Samuel to King Sha-ul in Samuel 15,3 where the king is ordered to destroy utterly all the possessions of Amalek.

תמחה את זכר עמלק THOU SHALT WIPE AWAY THE REMEMBRANCE OF AMALEK, — both man and woman, infant and suckling, ox and sheep (a quotation from I Samuel 15:3, stating how the Amalekites were to be destroyed), so that the name of Amalek should never again be mentioned even in connection with a beast, in that one could say: “This beast belonged to Amalek” (Pesikta Zutrata).