I found an absolutely beautiful Jade in a dumpster when I was tossing my trash. I pulled it out and after trimming a bit it was absolutely fantastic. I proceeded to over water it and practically kill it. It got so bad that I thought it was a goner...and then I did the unthinkable. I cut off the entire matted and ruined root ball. The whole thing. I let it air a few days and stuck it in an awful mixture of street dirt. 6-months later, it is making a huge comeback. I barely water it now and give it a shower every six weeks or so to blow away any mites or whatever crawlies happen on it. It is doing fine. I happened on another specimen with an 8-inch trunk and I broke it up to make about 5 new plants with 4-inch trunks (the 8-inch was rotting). I'm hoping to get at least 3 of those rooted using the same method. Re-rooting a 4-inch trunk gave me some confidence with Jades. They seem to be really resilient if you sorta be a little mean to them ;-)

Yes, you can cut. Feel the stem. Is it squishy? You will want to cut the stem back until you reach healthy tissue (start at the roots, of course). I see some brown on the stem. I would start cutting there, and work up. Keep cutting until you reach tissue with no black or brown. You want creamy white-green. After you finish cutting, dust with cinnamon to discourage disease and rot. Let the cut stem sit out of soil for a few days (in a dry, dim, cool place). the cut end will feel rough and hard (not moist or juicy). Put it in new DRY soil. I would suggest using 60% perlite and 40% cactus and succulent mix. wash the perlite to get out the dust. Don't breathe in the dust, either- it is harmful to the lungs. Prop up the stem in the soil with rocks, so it stays upright. In a few weeks, you should see roots :) Don't check often for roots, or you may break existing ones. It is best to wait until you see new growth, and then you can water a bit. The soil you have in the picture looks like it has a large contingent of peat. Peat holds water for a long time, and that rots the roots. By doing the above mix, you can avoid rot, but still be careful with watering. To check if you need to water, you can use a wooden skewer. Poke it into the soil, and if it comes out dry, you can water. Good luck! ~palmsandsnow

Most succulents do well in a mixture of commercial cactus and potting mix combined 50/50 with either perlite or Pumice from your nursery. However For this plant I am not sure such a fast draining mix would be needed. I hope someone can come along and let you know or maybe a Google search would give you more information about its planting mix and water needs. (I grow it in the ground and doesn’t seem particularly fussy about watering.)

No problem with your cutting have a small stem. Just lay it on top of your potting mix - after callusing a bit. I don't water until I see new growth or roots, so I sometimes only wait a day before "planting" on dry mix. This one is sitting atop the potting mix. It's a bit further down in the pot than I like, but I was afraid it would fall out. And here is why I was afraid it would tumble out of the pot. Short stem! As you can see, it is rooting just fine. So now I'll leave it alone for a month or two. Yours will do just fine. ;-)