If you want to extend the grasstato to being a little more bamboo-like, with big thick stalks as part of the above-ground portions, there is a whole wealth of things you can do with bamboo. New shoots are good for food for both people and animals (once treated, anyway--they contain a cyanogenic chemical in them that can cause a world of poisoning if they're eaten in the untreated form); grown stalks can be harvested and used exactly like wood in construction, decoration, textile making, and so on. Wikipedia, naturally, has a thorough but not exhaustive list of uses. There are many other such lists available, if you search for "uses of bamboo" on your favorite search engine.
If we're just talking what's actually known as "grass" though--and there's lots and lots of things that fall into that category, among them many of our cereal grains, sedges, reeds like water chestnuts and papyrus--there's still a whole bunch of uses they can be put to. Combining it with that ever-present horse manure in the setting and condensing it into bricks--for building or for burning--is one easy option. Then there's weaving it, to make baskets, thatch roofs, or fabric (grasscloth). The seeds can be used as food as well (this is, after all, how we get wheat, wild rice, and a number of other cereal grains), or fermented to make beer. Unfortunately one of the better uses of grass--sod bricks for building--probably will not work the grasstatoes, since sod relies on the propensity of grasses to make tight interlocking root networks and having random tubers in there would disrupt that.
As for the potato part, well--the uses of potatoes for vodka have been well-covered, but there are various and sundry other things you can do with them. In purely food-based uses, potatoes can also be rendered for starch that can be used for baking, or fed--either raw or cooked--to farm animals, though they can't be the only source of feed. Potato starch can also be used to make adhesives, and in a more modern setting, plastics. Since there's magic in this setting, you might be able to come up with a way to magically process grasstato tubers into potato-starch plastic--then imagine the sort of economic havoc the grasstato kingdom might be able to unleash as the sole producers of plastics in the setting. Then there's also some more mundane but still unusual non-food uses of potatoes that the people of your kingdom would also figure out, like using them in wound healing, or using water from potato boiling to polish up tarnished silver. (I'm trying to find a better reference than HGTV and Reader's Digest for these, but I can't seem to right now. Here are some links, though.)
Basically, both grass AND potatoes are fantastically useful, so there's a lot that could be done with them.