It was uttered by the Bishop commanding (!) a siege during the Albigensian Crusade, when confronted by one of his subordinate commanders who questioned the wisdom of torching an entire town that held orthodox believers as well as Cathars.
You do recall correctly -- the actual phrase is: "Caedite eos. Novit enim Dominus qui sunt eius.", uttered by Arnold Amaury, head of the Cistercian Order at the battle and sack of Bezier in 1209. Your translation is good.
However, a point is being missed here. First, this particular phrase was used in the Albigensian Crusade, which was not a holy war against Islam, but rather, the (ruthless) putting down of a Christian heresy.
But there is an even more relevant point -- my earlier one about the pitfalls of Whig history. You simply cannot project modern attitudes and assumptions retroactively onto medieval events. People in this time believed in their religion. Life was, as Hobbes put it, "nasty, harsh, brutish, and short." Abbe Amaury's shocking comment was meant sincerely -- he was not concerned about life in this world; it was infinitely more important that one be properly prepared for the next world. After all, life is temporary, while the afterlife is eternity. If it took the deaths of a few devout, believing Catholic brothers to wipe out a heresy (which put all of our souls in danger), "God would look after His own."
Primitive? Perhaps. I would put it differently. One might say, "positively medieval."