University President David Boren said in a statement the two students were dismissed for creating a "hostile learning environment for others." Their names were not released.
The video posted online shows several people on a bus participating in a chant that included a racial slur, referenced lynching and indicated black students would never be admitted to the university's chapter of Sigma Alpha Epsilon. A fraternity is an organization of male college students in the US.
"I hope that students involved in this incident will learn from this experience and realize that it is wrong to use words to hurt, threaten, and exclude other people," he said.
Boren said the university is working to identify other students involved in the chant, who may also face discipline.
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The video was taken on a bus going to an event at a country club. The person who recorded it has cooperated with the investigation, Boren said Tuesday ahead of a Board of Regents meeting.
In a statement emailed by his father, Parker Rice said the incident "likely was fueled by alcohol," but "that's not an excuse." He said he was "deeply sorry" for the performance, calling it "wrong and reckless," ''a horrible mistake" and "a devastating lesson" for which he is "seeking guidance."
He said he withdrew from the university Monday and that threatening calls to his family prompted them to leave their North Dallas home.
The parents of Levi Pettit posted a statement online saying they were shocked by their son's actions, that he "made a horrible mistake, and will live with the consequences forever."
She said she was "heartbroken" by the portrayal that she was racist but understood how the video must appear in the context of the week's events.
A "house mom" is a housing director who might oversee staff and finances at a sorority or fraternity house.