Open a mini XLR connector by removing the small screws on either side or releasing the rubber strain reliever from the port where the cable enters the connector. There will also be a small plastic sleeve inside this section -- be careful not to lose it, as it is important during re-assembly.
Strip off around 15 mm of the cable's outer insulation, using a wire cutter/stripper tool. Free the shield from around the bundle of wires inside. Twist it into a new strand. Separate the two wires inside by gently picking apart the twist or braid. Strip 5 mm of insulation off each of the internal wires. Slide plastic sleeve onto the cable, followed by the bottom portion of the connector case, as you will not be able to do this once you have soldered the connector to it. Ensure it is the correct way up to fit to the connector once soldering is complete.
Solder the twisted shield to pin 1 on the connector body; this will serve as the ground. When the solder has cooled, wrap the shield and the pin with electrical tape. The shield or pin should not be exposed anywhere along its length. Solder the two core wires to pins 2 and 3 respectively. Take a note of which color wire is connected to which pin. Allow the solder to cool.
Wrap a small piece of electrical tape around each connection to prevent any of the exposed metal from different contacts touching one another. Slide the plastic sleeve over the soldered connections, followed by the bottom portion of the connector. Tighten the screws. Repeat Steps 1-4 at the opposite end of the cable.