Door Pin Switch Connector, Wire Removal

you could yank it out with a plier, or if you can find enough room to work at the back of the switch you could solder the wire directly onto the back of the switch and feed the wire through the space that will be left when you remove the existing wire and terminal! 

From the looks of it it seems to be a relay clip, you could probably get one of those unshielded ones and re-crimp it to a piece of wire and re-connect it to the torn wire!