Find a container deep enough to hold the length of knife blade you'll be using. Fill it with water.
Clean the knife blade and the pruning shears with rubbing alcohol to sterilize them so that you don't introduce plant pathogens as you prune the plant.
Put on waterproof gloves, a long-sleeved shirt and safety glasses to protect your skin and eyes from the irritating sap.
Cover the work surface with newspapers.
Use the knife to remove stems on the outside of the plant. Grasp the top of the stem with kitchen tongs. Gently press against the three-angled stem to cut through the outer skin. Take about a 6- to 8-piece section if you intend to root the cutting. Remove the stem back to the main branch if you are pruning to shape the cathedral cactus or to keep it to size.
Dip the end of the cutting in water to wash away the sap, and lay it on the newspaper.
Wash the knife in the water before taking another cutting.
Use pruning shears to remove cuttings that are more toward the center of the plant, where it will be difficult to position the knife for a cut because of closely packed branches.
Wash the sap off the pruning tools and the kitchen tongs.
Roll up the newspaper so that any drippings of sap are to the inside, and discard it. Discard the water in the container, and wash the container with soap and water.
Remove protective clothing and safety glasses. Wash clothing and gloves, and wash off any sap from the outside of the glasses.