Unlike previous mice which could be unscrewed if you peeled off a label, these mice are GLUED together in a manner that appears to indicate no intention that they should be servicable at all. This irritates me, as does tossing stuff that can be fixed in the trash.
If you need to pay someone else to do this repair (because you don't have the skills or tools) you're probably better off buying a Mac-compatible USB optical mouse from another supplier for about half the price of a replacement Apple one - the repair is likely to cost you as much, and will probably need to be redone in another year or two unless you figure out a way to reduce bending of the cable. The one I've purchased (to have a spare for use while others are being repaired) has a much better strain relief than the Apple Pro Mouse, which should reduce wire breakage.
Start by prying the outer oval part off - it is easiest to start near the cutouts in the outer shell.
The inner white oval pulls out easily (you could start with that, actually)
Keep prying off the outer oval - I always find it beaks into several pieces.
Both ovals are off.
The inner shell is more difficult to remove. Observe the pivots; Here's close-up of one.
This shows both pivots.
You need to gently pry one of the pivot points on the base (clear plastic here) inward just a bit
to get the inner shell (dark plastic here) pivot to slip free so that the inner shell comes off. Do not pry hard and break something.
The cable, connected.
The cable, removed.
I only used the cutters to get the strain relief off the cable, and start stripping the jacket from the cable.
You can tell by the unnaturally sharp bends that the insulated wires have broken inside the insulation.
I have not cut the braid wires - they were completely broken.
Beware the color coding. It's more subtle than seems needful - best to repair one at a time and leave the others connected so there's no confusion, but under strong light you can tell the difference between the white and gray stripes on black wires. Soldering these together takes a reasonable degree of skill due to the small size of the wire. Remember to put heat shrink tubing on before soldering, and strip off enough outer jacket to put the heat shrink far enough away from the solder joint that it does not shrink before you want it to (while you're still soldering).