Disable skinning for a specific bone (For dismemberement)

I am using “Break Constraint” on a skeletal mesh to achieve dismemberement (Chop off the arm for example). It does work, and the arm does chop off, however it’s skinning is still connected to the rest of the body, so it sort of looks like it’s connected to the body with a jelly, or as if it is being stretched away from the body instead of being chopped off.

How can I disable skinning for a specific bone?

I know that I can just hide the bone, spawn a different skeletal mesh and hide all other bones on that one, but that will be much heavier on performance, especially considering that my main skeletal mesh has also clothing attached to it, and I want the clothing to chop off too.