The billionaire real estate baron, who is now running for president, sent a signed letter to the company's CEO and made threats about future policies.
Trump also took a swipe at CEO Randy Falco's management style.
"Also, it's too bad you didn't have the courage to call me yourself instead of delegating the task to Beau," he wrote.
The letter is the latest move after Trump said that he plans to sue Univision "for a tremendous amount of money" after they announced it will not air the pageant – which is partly owned by Trump – because of the disparaging comments he made about Mexican immigrants.
The Spanish-language broadcaster announced it will not show the July 12 Miss USA telecast. The pageant was slated to air on Univision’s UniMas network.
The announcement comes more than a week after Trump’s comments, which he made during a speech announcing his candidacy for president.
“When Mexico sends its people, they're not sending their best,” Trump said in the speech. “They're bringing drugs. They're bringing crime. They're rapists. And some, I assume, are good people.”
When asked by ABC News Thursday whether he regretted those comments, Trump said, “Not at all. I said it about people from all over. I didn’t say it about Mexico – I said people from all over.”
Univision Communications Inc. released a statement about the decision to drop the pageant broadcast.
"At Univision, we see firsthand the work ethic, love for family, strong religious values and the important role Mexican immigrants and Mexican-Americans have had and will continue to have in building the future of our country," it said.