Albert Barnes Commentary Deuteronomy 12:3

"and ye shall break down their altars, and dash in pieces their pillars, and burn their Asherim with fire; and ye shall hew down the graven images of their gods; and ye shall destroy their name out of that place." — Deuteronomy 12:3 (ASV)

Their groves - Understand this as their idols of wood; and see the note on Deuteronomy 7:5.