A technique used in the bind, in order to switch position below the opponent's sword for a position above the opponent's sword. I.33 recommends it when binding below and on the left. It is probably considered a safe action, so it is the first solution to the bind below and on the left that the manuscript teaches us. On the other hand it doesn't threaten the opponent in any way, so it doesn't give the opportunity to hurt him.
Mutatio gladii can be viewed as me leaving the bind (thus letting the opponent's sword out of control), but immediatelly returning back to control using a rebind. Because I have to expect the opponent thrusting at me as soon as I leave the bind, I should usually accompany the whole action with a step back - to keep the distance and gain time to finish my rebind, that will defend the thrust.