A joint sitting of the Senate and National Assembly began after Parliament opened a session earlier Tuesday to lay out the procedures.
The ruling party, ZANU-PF, said it planned to move a motion to formally expel Mugabe, who has been clinging on to the presidency despite a military takeover last week.
ZANU-PF, which Mugabe co-founded and led for decades, ousted the 93-year-old leader as its party chief on Sunday and gave him an ultimatum to step down in 24 hours or face impeachment.
The former vice president, Emmerson Mnangagwa, has joined those calling for Mugabe to stand down, in his first comments since the President fired him on November 6, triggering the political firestorm.
Ministers snub Mugabe: Mugabe called a cabinet meeting for Tuesday morning, but most members didn't show up, state media reported, in a further indication that his authority was ebbing away.
'Mugabe go home': Protesters gathered outside the Houses of Parliament, calling for Mugabe to quit, holding signs reading "Bob resign now" and "Mugabe go home."
Mnangagwa's whereabouts unknown: The former vice president's statement offered no clues about his location. Mnangagwa was named as ZANU-PF's new party chief on Sunday, paving the way for him to contest the 2018 presidential elections.
'The Crocodile' resurfaces
In a TV broadcast on Monday night, the leaders of Zimbabwe's military takeover said Mnangagwa had been in touch with Mugabe and planned to return to the country to discuss the way forward.
But in a a strongly worded statement from an unknown location on Tuesday morning, Mnangagwa said that he would not return until his safety could be guaranteed.
Mnangagwa -- known as "The Crocodile" on account of his sharp political skills -- enjoys widespread support within the military and is reported to have been in touch with army chiefs behind the scenes in recent days. But the apparent divergence in strategy indicated that they may not be moving in lock step.
"I told the President I would not return home now until I am satisfied of my personal security, because of the manner and treatment given to me upon being fired," he said in the statement.
He alleged "friendly" security personnel told him in November there were plans to "eliminate" him once he had been removed from his post.
Mnangagwa called on Mugabe to quit, and launched a thinly veiled attack on the President's cabal. "My desire is to join all Zimbabweans in a new era where corruption, incompetency, dereliction of duty and laziness, social and cultural decadency is not tolerated," he said.
His comments could be interpreted as referring to Mugabe's wife, Grace, whose lavish lifestyle and political ambitions alarmed sections of the ruling party's elite.
Mugabe's efforts to ease Mnanagawa out of the picture and position his wife as his anointed successor were a significant factor in the crisis. Six days after the military takeover, her whereabouts were still unknown.
'Time to go'
Thousands of protesters gathered outside parliament in Harare on Tuesday in support of Mugabe's impeachment, holding signs reading "Mugabe go home" and "Bob resign now."
At one point, protesters tried to storm the building, in frustration at what is becoming a long drawn-out process.
Others were more patient.
"We've waited for 37 years, we will do whatever it takes to make sure that he goes. So one more day or one more week is not going to make a difference," said Evan Mawarire, a pastor and activist, who described the moves to oust Mugabe as an exciting moment not to be missed.
"The fact is this -- the military has spoken, the people have spoken, parliament spoken, his own party has spoken. So, there's nothing left, he's all by himself."
Such protests are rare in Zimbabwe, where people had for decades been too afraid to protest under the country's oppressive rule.
But ten of thousands of people have shown up to rallies in the capital in recent days in support of the military's actions. Very few have voiced support for Mugabe, and foreign leaders also appear to be tacitly supporting moves to oust him.
On Monday, students at the University of Harare gathered to call for an end to Mugabe's rule, but they were wary of Mnangagwa, a man with a similar history to Mugabe's.
"We might be replacing a snake with another snake, that much ... we know," one student said. "What we're saying is we need new blood as our leader."