NGN is disputing the claim for libel, and said there is "overwhelming evidence" that he attacked Heard while under the influence of drink and drugs between 2013 and 2016.
The actor made the statements on Tuesday during his libel trial against United Kingdom tabloid The Sun, whom he is suing after the paper published an article in 2018 in which he was referred to as a "wife beater".
The first alleged incident of violence took place at Heard's home in March 2013 when he had "fallen off the wagon" and started drinking again after months of sobriety, and it was alleged he had struck her. She suggested it was about an ounce, but Depp said: 'I wouldn't say it was an ounce'.
While the Pirates of the Caribbean actor acknowledged his "illness", he told the court that Heard "never supported me in my attempt to be strong and avoid alcohol and drugs" and had seen his ex-wife take cocaine in front of him, The Guardian reported.
He had then slapped her three times because she had initially not reacted, Wass said.
"Asked why he'd apologised, Depp said he'd maybe done so that he'd stated something" ugly" or to placate her.
Asked by Ms Wass if he agreed he was violent in the clip, Depp said: "I was violent with some cupboards".
Afterwards, Ms Wass also read out a text sent by Mr Depp to his friend Paul Bettany on May 30 2014, which read: 'I'm going to properly stop the booze thing, darling.
Holding hands Amber Heard with her sister Whitney and lawyer Jennifer Robinson yesterday
The article accused Depp of abusing his former wife Amber Heard, a claim which the actor strongly denies.
NGN previously tried to have the case thrown out, but Mr Justice Nicol ruled last week the case could go ahead.
The couple first met on the set of the 2011 film "The Rum Diary", married in 2015 but divorced two years later.
In an unsent email composed by Heard in June 2013, three years before she publicly accused him of abuse, she said Depp had hurt her physically and that she did not know if she was dealing with him or "the monster" - his alter ego brought on by anger, jealousy and fueled by alcohol and drugs. He said she "would chop cocaine into lines and then put her finger into it and rubbed it on her gums". Depp said the message "doesn't make me feel very pleased with myself", adding "It is very disrespectful and disgusting in a way".
He added: 'The puppy got a hold of a little ball of hashish and just scooped it up before I could get to it'.
Johnny Depp is now set to reprise his role as the Gellert Grindelwald in the upcoming third Fantastic Beasts movie.
The Sun said the article refers to "overwhelming evidence" of domestic violence, referring to a previous USA court action by Heard.
Depp claimed that he resolved to divorce Heard after faeces were left in their bed.
Depp confirmed that it was, indeed, him howling on the tape, but that he was drunk and drawing sketches in his notebook at the time.
Mr Sherborne said: "The articles amount to a full-scale attack on the claimant as a "wife beater", guilty of the most horrendous physical abuse".