Here is my guide for disassembling the door mirrors without the need to cut any cables.
1. Remove door mirror from car. There are other guides that cover this so I won't detail that here.
2. The cable can be removed from the connector which will allow the cable to be removed easily
with out cutting any wires and also makes disassembly much easier. Here are a couple of photos
of the cables in the connector. Don't assume that all years/models have the same colour coding - make