I use sheep for mowing and pruning. They do an excellent job, it just takes management. You can mob graze them through an area and they will give an even cut to the grass and good fertilization. It helps to water after the sheep to get the nutrient into the soil and help the worms be more active.
The sheep need control to stick to their task or they will wander off to other areas. If they find a tree or shrub they like, they may strip bark. A strong fence that you can easily drag across the lawn works well.
Fence the area you want mowed and watch them closely. As their bellies fill up they will take longer to mow an area.
They can prune too but you have to watch to make sure they do not go too far or strip bark.
These sheep can easily keep this lawn mowed. You can see longer grass in the foreground, that is the next place I will move them to. If there are undesirable plants or weeds, I will let the sheep over-graze and trample that area and re-seed to grass if needed.
I put out way too much water in buckets and dump the water when I move the sheep to a new patch. Alternatively, you could run a sprinkler after the sheep.