Obviously a mower won't last much mowing over a rock pile but there are solutions out there that can handle rocks, just not sold in the US though.
Here is what we use in Europe:
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High strength Grade 80 chains do a fine job on rocks. It does require more HP and that's why we run narrow mowers than you in the US. I keep backing this thing over rocks and whatever is hidden under the brush and it just handles it fine. It also will do thicker brush easily.
Here is a video of me backing over a destroyed old house. Bricks, rocks, cement. By the noise, you'll notice when I hit something hard. One thing to keep in mind, is to have a fire extinguisher with you. This things can spark a lot and with dry brush, it doesn't take much to light on fire.
The chain skirts will do a good job on containing the debris.