The union said on Friday it had "received shocking news" three mineworkers were trapped underground at Beatrix's Shaft 4, with one rescued and the other two found and declared dead.
It believed the incident was due to a fall-of-ground, which it said was the most common cause of mineworker fatalities, causing 15 of the 39 deaths so far this year.
"They know that these things can be prevented but still the drive for more and more profit makes them risk the lives of black mineworkers," AMCU president Joseph Mathunjwa said.
"We again repeat our clarion call for the Mine Health and Safety Act to be amended so that these mining bosses can be held accountable [for fatalities]."
The AMCU had successfully fought for binding regulations earlier this year to protect mineworkers' safety amid the COVID-19 pandemic, as mines started ramping up after the country's nationwide lockdown.
Sibanye-Stillwater has been contacted for comment.
Its South Africa gold operations had achieved 11 million fatality-free shifts to March this year, which the company said at the time was a local industry record and "an unparalleled achievement for ultra-deep mining".
The gold unit had recorded "a fatality-free year for the first time in the company's history" in 2019, according to the company's annual report, following 21 deaths in 2018.
It had reported six fatalities at its PGM operations in South Africa in 2019 and said its US PGM operations had been fatality-free since October 2011.