Pence was delivering the commencement speech after receiving an honorary degree from the Catholic university, located in his home state of Indiana.
Videos showed some students standing as Pence took the podium, then walking out of the ceremony and gathering outside Notre Dame Stadium, where they held a short alternative "graduation ceremony."
Introducing Pence, University President Rev. John I. Jenkins said "political leaders are necessary for society, and we must strive with them to serve the common good."
Referring to "a fractured nation, with deep divisions and raw political feelings," Jenkins said injustice must be challenged; "But we must also listen to those who disagree, care for the bonds that join us together and find ways to build a society where all can flourish -- even the people who don't look like us, think like us, or vote with us."
Pence told the assembled graduates that Notre Dame was a "vanguard of freedom of expression and the free exchange of ideas."
"While this institution has maintained an atmosphere of civility and open debate, far too many campuses across America have become characterized by speech codes, safe spaces, tone policing, administration-sanctioned political correctness -- all of which amounts to the suppression of free speech," Pence said. "These practices are destructive of learning and the pursuit of knowledge."
He tweeted that he had been honored to speak at the ceremony.
Speaking on Sunday ahead of his graduation, Bryan Ricketts told CNN he would be walking out after learning solidarity during his time at Notre Dame.
Fellow protester Jenn Cha said it there needed to be space for dialogue between people of different beliefs. "However, it is an egregious insult to invite Pence to speak at the celebration of the accomplishments of university graduates, many of whom are LGBTQ, first-generation, low-income, and people of color he has actively supported legislation against," she said.
Liz Hynes said that Pence represented the kind of intolerance Notre Dame had sought to eliminate. "His anti-LGBT, anti-refugee, and anti-health care policies have harmed people in ways for which no religious justification can be made."
Pence is the first vice president to deliver a commencement speech at Notre Dame, according to the university.
Six presidents from both sides of the aisle have given commencement speeches at Notre Dame, including Barack Obama in 2009 and George W. Bush in 2001.
Pence received his bachelor's degree from Indiana's Hanover College and attended Indiana University School of Law.
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Some Notre Dame graduates walk out over VP Mike Pence speech - CNN