Late-night smash: Cyrus in trouble with U.S., Trump University

"Do you know what I heard on the way in today?" Letterman said. "[She's] been granted asylum in Russia."

Letterman then referred to Cyrus's recent performance at the MTV Video Music Awards.

"Did you see her Sunday night on VMA thing, the MTV show?" Letterman asked. "Oh man, the White House is considering military intervention."

Letterman proceeded to jab at Trump, whom New York Attorney General Eric Schneiderman accused of defrauding more than 5,000 people through Trump University.

"They got to sniffing around and they decided that the Donald Trump University was an unlicensed sham," he said. "And I thought, 'You know you're in a bad university when your commencement speaker is Whitey Bulger.' "

Letterman added that the students were guaranteed to get a picture with Donald Trump, but that never happened.

"They ended up having their picture taken with a cardboard cutout," Letterman said. "Ladies and gentlemen, I have met the man. I would rather have my picture taken with a cardboard cutout."