"I just remember saying, 'Oh God, not like this, no way,'" Miller said Friday, a day after the gray animal attacked him off Oahu's Bellows Beach.
The animal came after the 36-year-old attorney from Toledo, Ohio, in clear blue waters in an area not known for shark attacks. The last such incident in that area dates back almost 50 years, the state's Shark Task Force said.
The father of four was snorkeling and looking for turtles about 150 meters from shore when he noticed that fish near him looked spooked.
Then he saw a large shark's flat snout and felt the animal spin him around.
Speaking to reporters at The Queen's Medical Center in Honolulu, where he was taken after the attack, Miller said he punched the shark twice right below its dorsal fin, scaring it away.
Then Miller started screaming and yelling for help and headed for shore.
A day later, he was sitting in a hospital wheelchair, tired and nauseous from the pain medicine but grateful for his doctor's estimate that he should be walking in a few months and hopefully playing basketball with his teenage son in a half-year to a year.
"I'm happy — one, to be alive and two that I don't anticipate ... losing the leg," he said.
Miller still took care, despite his fatigue, to thank all those who saved him, including God, his doctors, the rescue crews, and the stranger named Ray who waded into the ocean to answer his cries for help.
"He's my hero. I would not have made it out of the water without his assistance. I owe my life to that man," Miller said.
Dr. Patrick Murray said the shark came down on Miller's leg and knee with "tremendous" force.
"It went right to the bone, into the bone, broke some of the bone, and into the knee joint and then removed a fairly large portion of his leg up by the knee," Murray said.
Miller has two wounds on the side and back of his left knee, one 3 inches to 4 inches and the other about 1 foot long.
Murray spent two hours operating on Miller's leg on Thursday. But he said Miller would need additional surgery to repair nerve damage.
Randy Honebrink, Shark Task Force spokesman, said the shark was likely looking for food when it came upon Miller. "The only way a shark can tell if something is a potential food source is by biting it," Honebrink said.
He said the attack was the first known shark incident in a coastal stretch from Makapuu to Kaneohe Bay since 1958. Earlier reports said the attack was the first at Bellows Beach in at least 16 years.
Miller said his 11-day vacation in Hawaii with his wife Lisa and his in-laws turned about "180 degrees" opposite from what he had planned. But he said he still loves the ocean.
"It's their environment. We're visitors to it," he said, adding, "All we can do is try not to look like food."