Morsi, deposed by the army in July, is already on trial for allegedly inciting the killings of opposition activists during his presidency, and faces two other trials which have yet to begin.
The ousted president on Tuesday will be tried with 130 other defendants, including members of his banned Muslim Brotherhood, the Islamist Palestinian movement Hamas and Lebanon's Shiite militant group Hezbollah.
In the footage, Morsi raised his hands in the air and angrily questioned why he was in the court.
"Tell me who are you!" Morsi shouted, jumping inside the cage. "Do you know where I am?"
- Egypt’s elections draw near amid unrest
- Egypt constitution approved by 98.1%
- At least 29 killed in Egypt protest clashes
The trial is being held under tight security in a makeshift courtroom inside a police academy on the outskirts of Cairo.
The Islamist leader was deposed by the army in July following massive popular protests against his one-year rule.
He also faces two other trials: one on charges of espionage involving Hamas which is due to open on February 16 and the other for insulting the judiciary for which a date has yet to be set.
Tuesday's hearing comes a day after the powerful military gave its backing to army chief Field Marshal Abdel Fattah al-Sisi to run for the presidency after he led the ouster of Morsi – Egypt's first democratically elected president.
The trial is part of a relentless government crackdown against Morsi and his Islamist supporters that has seen more than 1,400 people killed since he was deposed, according to Amnesty International.
Most of those killed have been pro-Morsi demonstrators in street clashes with police and his opponents.
The date of the start of the new trial is symbolic as Tuesday marks the third anniversary of the prison break that occurred during the uprising against Mubarak.
Prosecutors have said almost 70 of the defendants belonged to Hamas or Hezbollah and that some of the defendants were also accused of murdering police officers and helped thousands to escape during the jailbreak.
Morsi was among those who escaped from Wadi Natrun jail.