At least 78 people have died after authorities imposed a blockade on an illegal gold mine here, part of a monthslong standoff between prospectors and a government determined to force them to surface—often by cutting off their food and water.

The South African government has launched a rescue operation at an abandoned gold mine in the country’s North West province, where at least 109 men have died, a group representing the miners said, after local authorities cut off vital supplies in a dramatic bid to crack down on the country’s illegal mining trade.