Meaning of “Great is the weapon that cuts on its own”

Solution 1:

It is most likely the weapon can cut by its own weight. It can be said about a good knife. As such little effort is needed to saw through the pesky troll or hapless mundane. If you look at these pithy sayings for over a minute you are sure to overthink them.

Solution 2:

I'm assuming the game you're taking about is Darkest Dungeon. If you pay attention to when the narrator says that line, you'll notice he only says it when a damage over time effect (bleed, blight, etc) kills an enemy. The "weapon" cuts on it's own because you don't have to use an attack that turn to kill the enemy.