ORANJEMUND, Namibia—A dozen miles off the southwestern edge of Africa’s Atlantic coast, a 285-ton vacuum machine operating 400 feet below sea level is sucking some of the world’s most valuable diamonds from the ocean floor.

The $10 million crawler is part of a one-of-a-kind marine-diamond mining operation dubbed Debmarine Namibia. A joint venture between De Beers, a unit of Anglo American PLC, and the government of this sparsely populated desert nation, the marine mine has emerged as a rare revenue driver in today’s languishing...