Today I finally worked up the nerve to mow part of the back side of the dam. Here is what it looks like:

The uncut area in the back of the image is the very steep section that I did not cut. My techniques was to mow straight down the slope, make a wide pass to the end of the dam, then back across the dam to mow downhill on the next section. I never felt any instability at all. It would probably handle the steepest sections as well, but not with me on board.

And I have no intention of mowing the slope on the water side.