Lift the aloe vera from the old pot. Slide a knife between the soil and pot sides to loosen it if necessary.
Brush the loose soil away from the roots. Inspect the area surrounding the base of the main plant for pups, or smaller aloe plants.
Cut any pups that are taller than 1 inch away from the main plant, using a clean, sharp knife. Make the cut just below the soil surface.
Repot the main plant into a new pot that is one size larger than the old one. Use a cactus potting soil mixture or make your own mix by combining one part standard potting soil with one part coarse sand. Plant the aloe at the same depth it was growing at before.
Spread the cut pups out on a paper towel in a warm dry area. Allow the cut ends to dry and scab over for 24 to 48 hours before potting.
Prepare a 4-inch diameter pot for each pup. Fill the pots with a moistened cactus potting soil. Only use pots that have a bottom drainage hole.
Insert the cut end of the pup into the potting soil, pushing it in deep enough so it remains upright on its own. Water both the pups and the main plant when the soil begins to dry throughout. The pups form their own root systems within two or three weeks.