Sterilize a sharp knife, dipping it in alcohol or in a solution of nine parts water and one part bleach.
Cut the rootstock 3 inches above the soil line with the sterile knife. Make a straight horizontal cut through the cactus and discard the plant's top.
Slice a healthy stem off the cactus you intend to propagate. Choose a round piece with a 1-inch diameter, if available, to make it easy to fit it on the rootstock. This piece is known as the scion. Place its cut end on the cut portion of the rootstock, making sure some of the tissue from both plants is in physical contact. Use rubber bands going over the scion and under the pot to push the scion towards the rootstock. Remove them after both plant pieces become united, which takes one to two months.