SUPERIOR, Ariz.—One of the world’s largest untapped copper deposits sits 7,000 feet below the Earth’s surface. It is a lode that operator Rio Tinto PLC wouldn’t have touched—until now.

Not that long ago, an abundance of high-grade copper could be mined out of shallower open pits. But as those deposits are depleted and high-grade copper becomes tougher to find, firms such as Rio have been compelled to mine deeper underground.

Advances...