How to Take Cacti Cuttings
In general, taking cuttings from cacti is a fairly easy process. Some species are easier than others, but there are a few things one should keep in mind no matter the specie.
Make sure you cut will grow: With any cactus they need a place to grow from. The middle of the cactus where you see all growth come from is called the apical meristem. if this is not damaged, your cutting will eventually continue growing from this point again. If, for example, that growth point is damaged or cut (maybe you cut out a mid section of the plant, or the top was eaten by a bug or rotted) it cannot continue growing from here. When this happens the plant needs a new location to start growing from. With all cacti, they can only grow new offsets from their areole. An areole is special to cacti and is where you will see the tufts or spines emerge. Where the spines are, is where the new offsets will come from. If your cutting does not have at least one areole OR its apical meristem, the cactus will never be able to continue growth.
When making a cut, you MUST leave at least one areole and/or the undamaged apical meristem (growth point).
Making the cut: Depending on your reason for cutting, you must always ensure that your blade for cutting is clean. If your cactus is rotting and you are needing to make a cutting in an emergency attempt make sure you cut away all the rot. It is best to cut a few cm's above where the obvious rot is because it is likely the green flesh next to the rotted area is also infected with whatever is cause the rot. Play it safe and cut out extra when possible.
When cutting, I try to always cut on a diagonal angle. This is because when the cactus dries/heals, the skin will remain hard and rigid and not shrink much, whereas the inner flesh will dehydrate and shrink causing an indent in the top of the cut. When it rains, this "pool" will fill with water and can cause problems to that cactus with excessive water.
When you cut your cactus, we suggest using a rooting hormone. Many cacti will not need help rooting, they are fairly easy to root, but placing a *powder* (not liquid) on the cut surface will allow the cut to dry more flat, instead of curving in and making an indent on the cut site.
After the cut: Once you have cut, it is important NOT to let it get wet/moist. This means do *not* place the cut in water, and do not plant it in a pot. After cutting and placing the rooting powder on the cut, leave it in a well lit, but not direct sun, warm dry place. Leave it here for a couple weeks, to let the cut completely dry and heal. After this time (larger cacti can sit on the table for many months at a time without water), if healed, you may plant it in its new mix. Once planted do not water for a while. This is highly dependant on specie, so if its a slow grower that doesn't like water (Astrophytum, Ariocarpus, Lophophora, Turbinicarpus etc), do not water at all for a month or more. If it is a faster growing specie that can take some over watering (Cereus, Myrtillocactus, Hylocereus, Trichocereus etc) you may water it a *little* bit every few weeks. Once you see root buds forming (leave plants undisturbed for at least a month before checking) you may begin to water the tiniest amounts once in a while.
Cacti are able to last out of sand/soil for long periods of time. This is for 2 reasons. First, they have massive water storage in their body, so they can keep themselves going for prolonged periods. Second is that they are CAM plants and can take in moisture through their skin at night (humidity). When they have no roots, there is no way for them to take in water except their skin, so watering a plant with no roots is only going to lead to rot. It is like feeding a person with no mouth, the food will just build up around the skin and form a rash...cacti are the same, instead of a rash, they get rot. I would bet the number 1 killer of cacti cuttings are people water them and they rot.