Rose cut Jack’s hand off
To let someone cut you free from handcuffs with an axe would take a mad person, particularly if that person closes their eyes before the cut. Rose wasn’t supposed to make that shot, as you can tell if you pay close attention to how she swings the axe.
If it weren’t movie magic, she would have removed Jack’s hand by hitting the back of his hand instead of the shackles. That would also release him from his restraints, though maybe in a far more painful method.
