Depp, once among Hollywood's biggest stars, said Heard's allegations cost him "everything." A new "Pirates" movie was put on hold, and Depp was replaced in the "Fantastic Beasts" film franchise, a "Harry Potter" spinoff.
Heard's attorneys have argued that she told the truth and that her opinion was protected free speech under the U.S. Constitution's First Amendment. Closing arguments are scheduled for May 27.
Less than two years ago, Depp lost a libel case against the Sun, a British tabloid that labeled him a "wife beater." A London High Court judge ruled he had repeatedly assaulted Heard.
Depp's lawyers filed the case in Fairfax County, Virginia, because the Washington Post is printed there. The newspaper is not a defendant.