Rousey, 25, said she has trouble watching the clip because of its gruesome nature. In the first round of the UFC 140 tilt between Mir and Nogueira, "Big Nog" refused to tap after getting caught in a tight armbar.
Mir went on to break Nogueira's arm, as he earned a ref stoppage at the 3:38 mark of the opening frame.
"I was fortunate enough to meet Mr. Mir's little daughter, who is a new budding judoka," Rousey said. "I actually voted for his armbar. I thought it was the coolest one."
Rousey's armbar victory over Miesha Tate was up against Mir's win over Nogueira for submission of the year at the 2012 World MMA Awards.
Other finalists were Charles Oliveira vs. Eric Wisely (UFC on FOX 2), Rousimar Palhares vs. Mike Massenzio (UFC 142) and Chan Sung Jung vs. Dustin Poirier (UFC on FUEL TV 3).
"It's the only armbar I could not watch," Rousey said of Mir's bone-breaking submission of Nogueira. "I couldn't watch it. I'll watch mine over and over like it ain't no thing because that was a dislocation. His was an actual break, so I thought that was more diesel in my mind."