In Lord of the Rings, the Fellowship of the Ring heads into the Mines of Moria to escape from the Watcher in the Water after attempting to cross over the Misty Mountains.
Inside the Mines of Moria there are skyscraper sized halls and there are dozens of them miles and miles long. There is even a deep shaft that, I'm assuming, they used for mining various precious resources
I know we should just stop thinking about the small details and accept it as movie logic but, realistically, where in the world would they put the millions of tonnes of stone that they would inevitably end up mining out?
We know from the books that Moria is taken back after the events of the movies (an epic detail I was pissed they left out in the movies). They would continue the mining and find riches galore.
My best estimate is that they pounded the stone into gravel and transported it up to build roads. Or cut the stone perfectly to use as building blocks for other cities and fortresses (like Minas Tirith, Helms Deep etc.).
By my estimates from a couple pictures I looked up and the movies, there aren't enough stone buildings/gravel roads to even come close to matching what they hollowed out in Moria (not including the lonely mountain kingdom). They would still have so much stone they wouldn't be able to do anything with it.