It's a common misconception that the desert is barren with scarce vegetation. Saguaro habitat can include areas which are almost continuously vegetated, including palo verde and mesquite trees and all manner of grasses, shrubs and smaller cacti. There's a good pic in the article of an unburned area that shows this (about 1/3 down the page). Even in less vegetated areas, seasonal rains can cause bursts of growth that then dry out and fuel fires. Certain invasive species exacerbate this issue, as mentioned in the article.
1-2 foot chunks sectioned from a saguaro trunk will quickly die. The plant's "spongy interior" mentioned in the article will dry out if cut like this. Mature cactus can be transplanted but require special care and support as it takes a long time for them to get rooted. I'm not sure if saguaro arms or larger sections can be transplanted independently as "cuttings". Even if it's technically possible its not common as the mature plants are extremely slow growing and relatively fragile. There are also some state laws around removal and destruction of saguaros that would likely restrict a plan like this.