National Park Service spokeswoman Maria Gillett says Ed Hommer, a 46-year-old pilot from Duluth, Minn., was killed instantly when he was struck by a basketball-sized rock.
Gillett said rangers received a cell phone call just before dawn Monday from team leader Jim Wickwire of Seattle. He said one member of a four-member party on Disappointment Cleaver, at the 11,700-foot level of the 14,411-foot mountain, had been struck and killed by a rock.
Disappointment Cleaver is the most dangerous part of the climb, especially at this time of year when melting snow and ice have exposed more of the rock.
Park spokeswoman Lee Taylor said Hommer's body was removed by helicopter at midday Monday. The other members of the party hiked down to Camp Muir, at 10,080 feet, where they were met by a helicopter and taken off the mountain.
Hommer, who lost his legs in an airplane crash on Mount McKinley in 1981, used carbon-fiber and titanium prostheses and had hoped to be the first double amputee to scale Mount Everest.
Last October, his quest to scale Everest was called off when he and his team, hampered by bad weather, had to turn back 3,000 feet short of the summit.
Since he lost his legs, Hommer has gone on climbs in Alaska and the Himalayas. In 1998, he tried to climb Mount McKinley but was thwarted by storms and high winds. The next year, he reached the 20,320-foot summit, the highest in North America.
Besides Wickwire, the other members of Hommer's Mount Rainier climbing team were Tim Herlehy and Scott Rose, both of San Diego.
Wickwire, 62, has witnessed other deaths at high altitude.
On Mount Everest in 1982, Wickwire watched fellow Seattle climber Marty Hoey fall to her death.
And in his 1998 book, "Addicted to Danger," the veteran mountaineer wrote about crossing a remote Alaskan glacier when he and his climbing partner, 25-year-old Chris Kerrebrock, were pulled into a crevasse. Kerrebrock became wedged between two walls of ice. Unable to free him, Wickwire spent the night in his sleeping bag on the glacier's surface while his partner died 20 feet below.