Rot is your problem and water-retention is the cause.
Use your fingers to explore the stems of your plant. Forget the roots. If the stem is soft and mushy (healthy Jade stems will be really firm) follow that stem until you come to a firm area. Cut off at that firm part. Examine the cut end. Is it black or whitish? If black, cut off a bit more. You want to have the cut stem with no trace of rot (the black coloration). Continue to do that with each and every stem. You might end up with absolutely no rooted stems at all. The good thing is that Jade will readily root from these HEALTHY cut stems.
Any well-draining mix is fine, and that cactus mix will do well. When rooting the stems, first dip them in rooting hormone (whatever you can find in your big-box store), and then let them dry for a few days to a week to callus. Then, if you want just a single, multi-stems plant, put them in a single pot with your cactus mix, burying the stems approximately 1-2" deep. You might have to loosely bind then together and put a couple of stakes adjacent to them for support. Water the mix well and keep your pot in a shaded area. You don't want the mix to get a lot of water (only lightly water when the mix looks dry), so keep the pot in a protected area away from rain or a sprinkler system. If you want multiple plants, just use a stem or two in each pot. The pot size depends on the number/size of the stems. You don't want a too-large pot. If the stems are perhaps 6" in diameter (all added together), use an 8" pot. Any pot will do so long as it has plenty of drainage holes, but unglazed clay is probably the best. Clay is heavy enough to resist tipping over as the plants grow and is breathable. Be sure your pot(s) does not sit in water, like using a saucer under the pot and not emptying it.
You will know when/if your plants are rooting by new growth on your stems.
Good luck.
