Commentaire sur L’Exode 17:13

ויחלש יהושע AND JOSHUA DISCOMFITED [AMALEK] (more lit., he weakened Amalek) — he cut off the heads of his mighty men and left only the weak amongst them, and he did not kill all of them (leaving the weak men alive: thus Amalek was made weak, and powerless for further mischief). From this we may learn that they acted according to the expressed pronouncement of the Shechina (otherwise they would, in the stress of battle, not have so discriminated) (Mekhilta d'Rabbi Yishmael 17:13:2).

את עמלק ואת עמו, fellow travelers from other nations who had joined Amalek in his attack against the Israelites.

ויחלש, he defeated them. The word חלושה in the same sense occurs in Exodus 32,18 when Moses describes the noise he hears when descending from Mount Sinai as not being typical of the sounds one hears from soldiers suffering a defeat.