how to properly remove these cable connectors
In some (not all, depends on the crimp style) cases you can use pliers (or locking pliers such as vise-grip) to squeeze an "oval" or "flattened" crimp on the long axis, and that will open the hole enough that you can slip the wires out. If not, yes, you have to cut them off, as per the comment that @Steve should make into an answer.

If that does work, you still should plan on new connectors for whatever new wiring work you are doing, as "recrimping" used connectors is not very reliable.