The lawsuit is over an opinion piece Ms Heard wrote for the Washington Post in which she called herself a victim of domestic violence. He denies any abuse.
Ms Heard has sued back, with a $100m counterclaim against Mr Depp.
The closely watched civil trial, which is taking place in Virginia, is now in its second week.
Ms Heard's team has portrayed Mr Depp as an abusive partner prone to drug and alcohol binges.
Mr Depp's team has presented Ms Heard's claims of domestic violence as a "hoax" and a calculated strategy to ruin his reputation.