What ground cover can handle a blazing Mojave yard?

I’d start with plants native to your specific part of the Mojave, rather than aiming for a solid carpet. Indigo bush is one possible candidate, but check with a local native-plant nursery that it suits your elevation and soil. A few spaced plants with some open ground between them can look intentional and take less water.

For a softer, spreading look, prostrate rosemary or rockrose are worth asking about locally. They aren’t native desert plants, so don’t assume they’ll thrive without water while getting established. Plant in the cooler season, mulch the soil, and give new plants time to build roots before the harshest heat.

A continuous green cover may be a frustrating target in full desert sun. Gravel or wood-chip mulch between a smaller number of heat-tolerant plants is a perfectly reasonable design, and it avoids trying to force a lawn-like look where sparse planting may fit the conditions better. Keep mulch clear of plant stems.