The president emerged victorious in a similar motion and an impeachment vote earlier this year.
Mkhwebane’s most recent job was with the State Security Agency.
Africa’s Ebola epidemic has not run its course and around 30 people are still getting infected each week, says the UN special envoy for the disease.
With the economy in a precarious state, and the load-shedding crisis adding to the country’s woes, President Jacob Zuma is under pressure.
The union has accepted a wage offer from employers but will continue striking over conditions relating to future pay negotiations.
The cash-strapped armed forces are in a "critical state of decline" that will take at least a decade to fix, according to the SA Defence Review.
Worker strikes at car and vehicle part manufacturers have impacted negatively on production lines at South African automakers.
A man died after he was hit by a rubber bullet during clashes between police and striking farmworkers in the Western Cape, said a police spokesperson.
Three transport unions have agreed to abandon their industrial action but Satawu, which represents about 28 000 workers, says it will continue.
Deputy President Kgalema Motlanthe says SA is looking to Nigeria for oil, suggesting Pretoria cut crude imports from Iran to avoid looming sanctions.