Mary Strause, a filmmaker in Wisconsin, logged on to Amazon’s video-streaming service in late May so she could share a link to her latest project, a docuseries that harshly criticized the U.S. health care industry. She was surprised to see that her video had vanished.

Ms. Strause had no way of knowing it, but the video had been taken down after a law firm working for UnitedHealth Group, one of the country’s largest health care companies, sent a letter warning Amazon and another streaming service, Vimeo, that the video was defamatory.

It was the latest salvo in an aggressive and wide-ranging campaign to quiet critics. In recent months, UnitedHealth has targeted traditional journalists and news outlets, a prominent investor, a Texas doctor and activists like Ms. Strause and her father, who complained about a UnitedHealth subsidiary.

In legal letters and court filings, UnitedHealth has invoked last year’s murder of Brian Thompson, the chief executive of the company’s health insurance division, to argue that intense criticism of the company risks inciting further violence.

The tactics have had an impact. Amazon and Vimeo both removed Ms. Strause’s film. The Guardian postponed publishing an investigation of the company after UnitedHealth sued over a previous article it said was defamatory.

UnitedHealth joins a growing group of companies and wealthy individuals, including President Trump, who are using legal threats and lawsuits to deter or penalize criticism.