CAPE TOWN, SOUTH AFRICA -- The only mixed-race member in the South African Cabinet announced yesterday that he was resigning, while tension in the gold mine strike increased with the deaths of three black workers.

The Rev. Allan Hendrickse, a Cabinet member without portfolio, accused President P.W. Botha of insensitivity. Botha frequently has castigated Hendrickse for criticizing racial segregation laws and governmental crackdowns on black protests.

Hendrickse told the House of Representatives, which Botha set up in 1984 for people classified as Colored (mixed-race), that the president's attacks prompted his resignation. His departure leaves only one nonwhite, East Indian Amichand Rajbansi, in the Cabinet.

Meanwhile, three black workers were killed in violence at the mines. Owners called for negotiations to avert further deaths. The Anglo American mining conglomerate said the two-week-old dispute over wages appeared to be crumbling and suspended a threat to dismiss another 16,000 strikers.

One worker was killed before dawn at the President Steyn mine near Welkom. Strikers, blood oozing from wounds, said mine security guards burst into a hostel and fired rubber bullets in an attempt to force them to return to work.

Two others died in weekend clashes between strikers and miners wanting to resume work at Western Areas, a gold mine south of Johannesburg, mine owners said.