The complaint, filed in federal court in the Northern District of Texas, alleges the network aired two different responses from Harris responding to a question about the war between Israel and Hamas in Gaza.
The version that aired during the "60 Minutes" program on Oct. 6 did not include what the lawsuit calls a "word salad" response from Harris about the Biden administration's influence on Israel's conduct of the war.
"Former President Trump’s repeated claims against 60 Minutes are false," a CBS News spokesperson said. "The lawsuit Trump has brought today against CBS is completely without merit and we will vigorously defend against it."
Trump and Harris face each other in what polls show to be a tight race ahead of Tuesday's U.S. presidential election.
The suit demanded a jury trial and about $10 billion in damages, the filing showed. It alleges violations of a Texas law barring deceptive acts in the conduct of business.
Trump has repeatedly assailed the network on the campaign trail over the episode and has threatened to revoke CBS's broadcasting license if elected. CBS has said Trump backed out of his own planned interview with "60 Minutes."