STORY OF SEASONS: Pioneers of Olive Town

During the tutorial, Victor will give you most of your tools to help out on the farmland, including the hammer. From this point, use the hammer to break any rocks that you come across, whether it be from running through the mines or just clearing your farmland itself. These can be populated with different minerals ranging from actual stone up to the rare and elusive Orichalcum Ore. You can track this in two ways:

1) On the Title Screen, go through the trophy icon to find all tracked trophies. Trophies with cumulative progress can be tracked from here.
2) In-game, go to the Records page of your menu and choose Change Title. Interact with the Mining skill menu and you'll be able to see, among the level titles, some titles offered for breaking a certain amount of stones.