Protect yourself from the sap of the cactus before working with it. Wear gloves, eye protection, head protection, long sleeves and pants. Prevent any sap from coming into contact with your skin; absolutely do not allow any to get into your mouth.
Remove the cactus from its pot by gently tilting it upside down with one hand while holding the rootball with the other. Set the plant aside. Line the bottom of the new pot with about 1 inch of gravel. Place enough cactus soil in the new pot to bring the plant's crown to the same level it was in the previous pot. Sit the rootball in the pot and gently pack the new soil in around it. Water the plant thoroughly.
Replant cuttings by first removing sections of the firestick with bypass pruners. Lay the sections out two or three, until the bottoms have scabbed completely. Prepare a pot with a 1-inch layer of gravel in the bottom and enough loose cactus mix to fill it. Push the scabbed cuttings into the soil mix and firm the soil around them. Water the cuttings.