US military prosecutors say Hamdan moved the al-Qaeda leader before the attacks.
Hamdan, who is about 40 years old, is accused of conspiracy and of providing material support to terrorism, and faces a possible sentence of life in prison if found guilty.
The Yemeni was captured at a roadblock in southern Afghanistan in November 2001, allegedly with two surface-to-air missiles in his car.
He says he drove for bin Laden in Afghanistan because he needed the $200 in monthly wages but denies joining al-Qaeda, pledging loyalty to bin Laden or participating in attacks.
Hamdan has already spent six years in prison at the Guantanamo prison camp.
Defence lawyers have said that Hamdan was subjected to abuse while in US custody, including humiliating interrogation tactics and sleep deprivation.
Several witnesses, including Khalid Sheikh Mohammed, the alleged senior planner of the September 11, 2001, attacks, said Hamdan had no knowledge of attacks by al-Qaeda, including the September 11 attacks on New York.
“He was not fit to plan or execute,” Mohammed, who is also due to be tried by the tribunals, said in written testimony.
“Hamdan had no previous knowledge of the operation, or any other one,” he wrote.
“He is fit to change trucks’ tyres, change oil filters, wash and clean cars.”
Five men, including Mohammed, were charged with crimes relating to September 11 attacks in July.
The administration has faced heated criticism over the Guantanamo Bay prison camp and the special tribunals, which operate under different rules to otherr civilian or military courts.
Only a small group of authorised observers and journalists are allowed into the small courtroom and military authorities prohibit the proceedings to be recorded by television news networks.
The trial continues.