The 57-year-old Depp is suing News Group Newspapers, publisher of the Sun, and the paper's executive editor, Dan Wootton, at the court in London over an April 2018 article that called him a `wife-beater.`
The Hollywood star strongly denies abusing Heard.
In the first session of her testimony that is expected to last for three days, Heard denied accusations that she was a heavy drug-taker and drinker as well as being controlling and abusive herself.
She also described an incident in January 2015 in a hotel room in Tokyo over a pre-nuptial agreement between herself and Depp, and suggested there was an argument about it.
She testified there was an argument in a hotel room in Tokyo that resulted in Johnny kneeling on her back and hitting her on the back of the head.
In written testimony released as she took to the witness box, Heard said she worried Depp would kill her at various times during their relationship that saw her enduring `punching, slapping, kicking, head-butting and choking.`
She also said `some incidents were so severe that I was afraid he was going to kill me, either intentionally or just by losing control and going too far.`
According to the 34-year-old Heard, Depp quote - `explicitly threatened to kill me many times, especially later in our relationship` and that he blamed his actions on `a self-created third party` that he referred to as `the monster.`