M-Class 2001 Spring Trip to Death Valley
We had two flat tires. One was a sidewall puncture, most likely caused by a small stick (remember, bushes in the desert grow very slowly and develop an incredibly hard wood - as hard as nails) we fixed it with a Safety Seal plug.

The other tire damage was more serious.
It was compression cut, caused by driving (too fast) over a rock as depicted below. The tire sidewall is cut between the rock and the rim. This usually happens when you try to avoid a rock (but don't succeed) and hit it only with a small portion of the tread. Most of those damages occur on one of the right tires - in our case it was the front right tire. There is no field fix for this kind of damage.

These accidents happen because it is not easy for novice off-raod drivers to spot rocks that could endanger the tires. Rocks like the ones you see below are "icebergs" - only 10% of their body shows. The only warning sign is that they are somewhat blackened on the edges - blackened from other people's tires.
Don't try to avoid them. You might fail. Drive slowly with the center of your tire(s) over them to avoid compression cuts. See how

The rock blelow might cause a compression cut as described above but when you try to avoid the rock you might not succeed completely (usually your front tire will clear the rock but the left rear might scrape with the sidewall). That will eventually kill the tire.

Notice how the inside (right) of the rock is all black - black from sidewalls scraping alongside the rock. The rock does not really care, but your tire(s) will suffer - and it might even blow out.

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