Univision said last week it would not air the July 12 pageant because of what it called insulting remarks about Mexican immigrants made by Trump when he announced he was running for the Republican presidential nomination.
In a rambling 45-minute speech, Trump said "when Mexico sends its people, they're not sending their best".
"They're sending people that have lots of problems, and they're bringing those problems with us," he said.
"They're bringing drugs. They're bringing crime. They're rapists. And some, I assume, are good people."
Trump's comments triggered criticism both in the United States and Mexico, with Mexican Interior Minister Miguel Angel Osorio Chong calling them "prejudiced and absurd".
Hispanic and migrant advocacy groups slammed Trump, while Democratic presidential frontrunner Hillary Clinton called his remarks inflammatory.
But Trump is not backing down, posting a series of tweets reiterating his views.
Networks NBC and Televisa also severed business ties with Trump over the comments.
It means the Miss USA and Miss Universe beauty pageants - for which Trump owns the broadcast rights - will not be aired on NBC.
And Trump, 69, will no longer appear in the NBC reality show The Apprentice, on which he had been a star attraction.
Just hours later, Mexico's Televisa - the world's largest Spanish-language network - also announced its decision to cut business ties with the billionaire property developer-turned-TV star.
NBC and Televisa's announcements came four days after Univision, the leading broadcaster in the US Spanish-language TV market, broke with the Miss Universe Organisation.
Trump believes Univision and NBC are trying to suppress his right of free speech.
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