If you are staying at Villa Mimma and are looking for a food store, you have various options. In order of size, from the tiniest to the biggest, here are some ideas, although the best way for you to know the area is to take a drive and see where it takes you:
1 - Treville
There is a butcher with the most wonderful meat, ham and salame (he makes them), ravioli (made only on some days or on order) and a deep freezer with ice-creams, pizzas, vegetable, etc.
Also, there is "La rata birata", which is a wine-bar that serves hot-meals and that also has a small food section with fresh produce such as cheeses, bread, milk, butter and basic provisions. It has also pasta and sauces!
2 - Ozzano (2km from Treville)
If you want a bit more of a choice and some fresh fruit and vegetables, Ozzano is your nearest option. Along the main road that cuts through the village, there is a food store that has everything. It is very small compared to a supermarket, but has all you need.
3 - Supermarkets
Well, for a proper supermarket you are spoilt for choice if you are prepared to drive for 10-15 minutes. You can either go to Casale to the Iper-Coop (a real shopping centre) or you can go towards Asti-Moncalvo and stop at the Penny supermarket, which faces a Gulliver supermarket, where you can find all you need.