It may survive, but the risk now is fungal infection. The damaged area and roots look wet. It is imperative that you let it dry in the air in a shady place. Do not repot until the wounded areas are calloused. A topical fungicide might be helpful.

Brad

That doesn't look [i]too[/i] bad. Clean the area of all the loose dirt (you can use water for this part. Boiled and cooled is clean enough) and pack some tissue into it for a few hours. Then hit it with some antifungal powder (ground cinnamon or sulphur) and leave it alone to dry fully. You'll lose some more areoles around the wound and it'll look even worse and possibly pull the plant to one side, but if it's not rotting it isn't a problem.

After that, I wouldn't repot it at all, at least not in soil. It's not going to do anything else this year unless you're in the southern hemisphere, and it'll sit happily in a pot of dry rocks until the spring. I've used plain sand to overwinter late purchases because it's very easy to pour in around the roots, but unless the roots are bone dry already using sand is a very bad idea.

Thank you so much for the responses Brad and sutremaine!

@Brad the area looks wet, because I washed it just before I took the photo. I was so shocked, I just grabbed the scissors, dug that slug out of there and rinsed the cactus under the water. I did not use sterilized water and I did not let it dry first, I just dumped cinnamon on there! (I knew about that from reading on this forum about Desert Rose pruning ) So, I hope that will be okay...
Can either of you please tell me, do I take all the soil off the roots and leave it like that in the air or what. Sorry, I am a total novice when it comes to cacti.

@sutremaine: I am actually living in the Virgin islands, so the seasons do not matter, it's warm all the time.
So, what type of mix can I repot it in? We do not get 'cactus mix' here, so it would be helpful to know what to mix together. I've had it in garden soil, mixed with sand, is that bad?
You are correct, the little cactus is already pulling to the side, so sad...

Thanks again for the help!

The cinnamon powder (or any antifungal) works better when dry. Fungi need moisture to survive and cinnamon is not strong enough to nuke them in all conditions, so the more inhospitable the environment the better. You can try drying it off with some tissue, but any water will be tightly bound up in the powder. Do you have a hairdryer with a 'no heat' setting?

Cactus mix is not about the ingredients themselves, but what they do for the plant. Sand is bad because its individual particles are small enough to hold onto water so that there's no air between the particles, and because the sand particles themselves are non-absorbent rock there's no air held inside them to compensate. Garden soil is also bad, and for the same reasons. The primary problem here is drainage -- if the sand / soil mix is in a raised bed or elevated part of the garden, then water can move both vertically and horizontally and not hang around the plant roots. In a pot where the mix is connected to the ground either directly through the drainage holes or via a wick, the water will pass down through the pot and be taken up by the ground. In a free-standing pot, it will be held in the pot (because the ground is more absorbent than the air) and cause problems.

The basic gritty mix popular on the GW forums is 1 part pine bark, 1 part calcined clay, and 1 part grit. All of these ingredients are between 1/8" to 3/8" in size, with the lower bound being the most important because 1/8" is the size at which the particles can't hold water up as well as gravity can pull it down. The calcined clay is porous and holds water within itself, where it is available to the roots but not forced on them. By itself it can be rather wet, especially when the pores are filled and water starts clinging to the outside of the pieces, so the grit is used to reduce the amount of water the mix can hold. Bark has air / water-holding properties somewhere between calcined clay and grit and is generally the cheapest ingredient once you can find it in the right size.

I say all this because I don't know your options where you are, so if you know why the gritty mix is made up as it is you can make something up without having access to the default materials. Cat litter sometimes comes in calcined clay form. It's pinkish-beige and rounded, and on the bag it might have a note about turning your cat's paws pink. Over here it often comes in a pink bag.

Depending on what fertiliser you're using, you'll also need some gypsum for calcium and Epsom salts for magnesium, plus a source of whatever nutrients aren't in the fertiliser. This isn't as critical for cacti as it would be for something like a food crop, since they're slow-growing and don't need much fertiliser.

I'm not sure what to tell you about your seasons, or rather lack of them. If in doubt, remove the soil from the roots (which you'll need to do anyway if you start using something grittier) and keep it dry, shaded, and out of strong wind.