sagebrush & other woody materials make excellent mulch. You do not need to chop it fine. The branches can be laid around the plants in short cuttings less than 12 inches. You do not need to measure. lol. Also any cuttings from other plants & weeds (before it forms the flowers) & leaves can be laid as mulch. Use whatever you can get a hold of.
You do want to want your wood chips to be very fine as this will seal the top layer of your mulch & your rain will run away instead of soaking in. Ex
Sep Hozier who "invented"
hugel culture does lots of work too in dry lands of Spain & Portugual, so you just have to understand the difference of hugel culture in dry lands compared to wet lands and adapt your techniques.
If you
land has some areas where more water washes over it because of the slopes then that might be a good location for hugel culture because it gets more water than just the rain water on that given surface. You could use swales to divert some of the rain water to your hugel culture.
If you do not have much access to woody material, then look for other organic material that will work. You only do hugel culture if you have the resources as there are other
permaculture techniques that may make sense for you in your climate.
Plus, plant the type of plants that will thrive in a desert, not the the water hungry plants that are high maintenance for your climate.
Brad Lancaster books & resources (videos, podcasts and website are good resources in general for growing in desert climates as he explains lots about water harvesting in desert climates.