On Tuesday, Storey spoke at the annual Stand Up for Heroes benefit, presented by the New York Comedy Festival and the Bob Woodruff Foundation. The foundation was created by Woodruff, the ABC news anchor injured in Iraq in 2006.
Stewart told Muir Tuesday that the event was like a yearly get-together.
"You get to see people progress through their recovery ... You follow through their ups and downs and it becomes personal," he said.
Since his injury and rehabilitation, Storey has run track in the Paralympics and completed the Marine Corps Marathon. This summer, he reached the top of Mount Kilimanjaro in Africa, in collaboration with the Bob Woodruff Foundation and the #Give2Veterans campaign.
He told Muir that his biggest highlight since losing his leg, however, was reaching the summit of Mount Vinson in Antarctica in 2013.
"To realize why you're doing what you're doing and really understand that 'Why?' factor. ... [It] pushes you to keep going and never quit no matter what you're doing," Storey said.
The next Woodruff Foundation fundraising event, "Dine Out for Heroes," will be on Nov. 11 in New York City. Visit bobwoodrufffoundation.org for more information.