He made the declaration at a rally where his wife Grace was booed by some party supporters.
￼Mnangagwa, nicknamed ‘the Crocodile’, is one of the top candidates to suceed Mugabe.
But Grace Mugabe has also been tipped to take over from her husband.
Mnangagwa, 75, was appointed vice-president in 2014 and has been widely touted as the obvious successor to Mugabe, who has led the country for 37 years.
At the weekend, Mugabe lambasted his vice-president, sitting nearby, when speaking in Shona in the opposition stronghold city of Bulawayo, Daily Mail reports.
“We are denigrated and insulted in the name of Mnangagwa. Did I make a mistake in appointing him as my deputy?” Mugabe asked.
“If I made a mistake by appointing Mnangagwa… tell me. I will drop him as early as tomorrow. We are not afraid of anyone. We can decide even here,” he said.
“If it has come to this, it is time we make a final decision,” he added, telling Mnangagwa and his supporters they were free to leave ZANU-PF.
“You can go ahead and form your party because we honestly cannot have this. We cannot be insulted on a daily basis.”
Some rally goers heckled Grace Mugabe, chanting at her “you know nothing” and “you are too junior” as the First Lady spoke before a section of the crowd that broke into a popular local song “oyenzayo siyaizonda” which translates to “we hate what you do.”
She shouted back at the hecklers: “If you have been paid to boo me, boo, go ahead…I don’t care, I am powerful.”
She then repeated her ambition to be appointed her husband’s deputy.
“Even if I become vice president, is there anything wrong with that?”
Mnangagwa was last month stripped of his role as Justice Minister, in a cabinet reshuffle widely considered part of a campaign to reduce his powers and quash opposition within the government.