Right, couper le souffle. Let's pull out the old pocket dictionary here:
à couper sûr, certainly
coup de chance, lucky hit
coup de fion (slang) finishing touch
coup de pied, kick
coup de poing, punch
coup sur coup, one right after another
...and 20-odd more, but no couper le souffle. No, wait a minute, folks, here's Google translator with “couper de souffle” = “breath.” Well, so much for my old pocket dictionary.
But it still doesn't make a lot of sense.