Sforno on Deuteronomy 13:16/ספורנו על דברים י״ג:ט״ז

1ואת בהמתה לפי חרב, to wipe out their memory as a form of vengeance on behalf of the G’d of Israel. The principle underlying the destruction of the belongings of these people is the same as that contained in G’d’s commandment to destroy every vestige of Amalek in order to obliterate any memory of that nation. (compare. Deut. 25,19) The prophet Samuel spelled this out prior to ordering King Sha-ul to carry out this commandment in Samuel I 15,3.