You can do anything you want with it, the cutting would certainly survive being chopped up some more.
However, I would stick it in a pot of dry porous soil and wait for it to establish roots first, that way it will have a chance to recover slightly. Once you have an established plant you can take as many cuttings as you want, you can even cut it down to a stump and it'll put out new growth, so there's no hurry for now.

Below is a link to another thread detailing the rooting of a cutting. You can follow the same advice given in that thread. The important thing is to not water the cutting before it has established roots or you risk rotting.

There're lots of other posts on this forum detailing the care and feeding of jade plants, so go ahead and search for "Jade plant" or "Crassula ovata" if you're interested.

Here is a link that might be useful: Jade cuttings

I forgot to mention:
1. Yes, those are roots forming on the sides of the branches. That is normal and generally a good sign that the cutting is healthy.

And 2. Those brown bumps on the sides of the trunk are axillary buds, they'll grow into new branches once the cutting has rooted and begins to grow. You can stimulate their growth by pinching the apical bud once the cutting has rooted.

Okey dokey. I'll just wodge this in my succulent mix as is and let it go, I guess. Won't water until I see new growth. We'll see how it goes! Thanks :D

D,

It would promote growth if you mist the cutting lightly every few days.

like, the leaves/stalk? or the soil?

or both? :D

The leaves/stalk only - the soil needs no water yet.

Excellent! I shall do exactly that then.