How do they mow grass on a dam?

Duh! they use a damn lawn mower.

My guess is that a crew using climbing gear and as @noelleptc posted, weedwhackers, would be used.

They use specially designed mowing tractors with very wide wheelbases, low center of gravity and rollover protection. Here’s an article from my favorite periodical, Turf Magazine, that explains how the crews that mow the aqueducts and reservoir dams around NYC do it.

Goats ?
@thorninmud great citation. Is that really your favorite periodical ?

@dabbler Well, there’s also the Journal of Maritime Law and Commerce, but Turf Magazine has a better crossword puzzle.

That could be prime grazing for a lot of sheep, especially those that live in mountainous terrain, for example… (has to be seen to be believed).

@WasCy: Seeing those pix is a good way to end my day. Extraordinary

@WasCy We used to tell the tourists in AK who asked how the goats could stand upright on that kind of slope that their legs were shorter on the side facing the wall. They were born either right-facing or left-facing goats and could only go one direction.