Have you ever seen grass? It rarely grows cleanly like it does in the game.
After some while, it will get seriously overgrown.
This should happen in the game too.
You would then have to either mow your lawn, or let some sheep and cow free to eat it off.
Lawnmower could work kind of like a plow.
In this manner.
You could probably also cut it with shears by hand, tile by tile, if required.
In addition maybe you could then collect and dry this grass to feed your animals.