Yes, Christmas cactus can be propagated through cuttings. To propagate a Christmas cactus, take a healthy stem from the plant and cut it into sections that are about 2 inches long. Each section should have at least two leaves. Let the cuttings dry for a day or two, and then plant them in a well-draining potting mix. Keep the cuttings moist, but not too wet, and make sure they have bright, indirect light. In a few months, you should see new growth on the cuttings.