The siege, which began in August at the mine in the town of Stilfontein, about 150km from Johannesburg, cut off food and water supplies for months in an attempt to force the miners to the surface so that they could be arrested.
On Monday, authorities used a metal cage to begin recovering men and bodies from the shaft, in an operation expected to run for days.
"We don't know exactly how many people are remaining there," South African Police Minister Senzo Mchunu told broadcaster eNCA.
"We are focusing on getting them, assisting them out."
It was difficult to say when all the miners would be brought up, he said, adding, "When each one of the miners who are underground went there, no one was counting."
In a statement, police said 51 bodies had been retrieved by Tuesday night, following nine the previous day.
The 106 survivors pulled from the mine on Tuesday were arrested for illegal mining, swelling the figure of 26 a day earlier.
For decades, South Africa's precious metals industry has battled illegal mining, which costs the government and industry hundreds of millions of dollars a year in lost sales, taxes and royalties, a mining industry body estimates.
Typically, it is centred on mines abandoned by companies as they are no longer commercially viable on a large scale.
Unlicensed miners go in to extract whatever might be left.
The South African government has said the siege of the Stilfontein mine was necessary to fight illegal mining, which Mining Minister Gwede Mantashe called "a war on the economy".
But residents and rights groups have criticised the crackdown, part of an operation called "Close the Hole".
