Okay this idea is going to mix a some bits about mechanics, mining, and stockpiles. I'm going to start with a very rough synopsis and then explain it. I hope it all makes sense.
Ready? GO!
When mining, each new space of earth contains 7 stone in there (like water for sake of argument). Mining skill determines how many stones are actually left over in the space. 7/7 stone piles can not be traversed and a conveyor belt can be used to remove mass amounts of stone from mining. Stone begins to pile at the end of the belt or somewhere else and after 7 of 7 stones fall onto the same space, that 'pile' topples into another space making two piles of 4 and 3 (or some such). This can continue as the pile grows larger and could potentially go up in Z-levels. Rock grinders can attack the stone to turn it into dust/powder/concrete mix (the Romans had it!)
And now for something a little more explanatory:
People have been asking for more realistic or challenging mining so it's not as simple to carve out a mountain home when your population is less than 20. So if stones could pile up in a space during mining and block passage, they would need to be moved by dwarves, or machines and this could provide more of a challenge. A mining conveyor belt would be perfect for this and it's really simple tech. Axles, belt, done. I felt the need to mention the stone piling up so that we can avoid one space of 284368812 stone that dwarves could walk through with no problem. I checked one of my dumps once and one space had a metric ton of stone that people were casually walking right through. I imagine some magical tower of perfectly balanced stone. But back to the idea... As stone topples over it takes up space and piles up. A rock grinder could be set out far enough away from the pile so that whatever "topples" into range could be ground up into a 'powder' and used for whatever. Some have mentioned sand for glass, personally I like the idea of concrete, though I feel that's not entirely dwarven.
This is just an idea that spans multiple suggestions and any feedback is appreciated. It probably isn't perfect but I liked it pretty well.