Hello.

They're not removable and that connector is an integral part of the underdash wiring harness. Your best bet would probably be to butt-splice the wire itself back together, if I'm understanding the problem. The wire itself is broken but the piece sticking out of the connector still has good contact? If yes, then patching the wire back together would be the way to go until you are ready to replace the entire underdash harness, which is something that you might want to consider if the wiring is so brittle that it's snapping off when you mess with it. Hope that helps.
