Mr Wilcox, aged in his 50s, died at the scene despite desperate attempts by his rescuer to revive him. Mr Wilcox was bitten on the right leg by what is believed to be a great white shark at Clarkes Beach, on the NSW far north coast.
Onlooker Mark Hickey rushed into the water with his surf-ski and dragged the man on to the beach where he gave him CPR for 20 minutes.
Mr Hickey, a Newcastle lawyer, said he saw a 1.8-2m shark menacing the victim.
"I saw what looked like seaweed but it was blood in the water," he told News Corp Australia.
"The shark came back to him and had another go. I didn't know it was a person but when I realised I ran out and waded to the bank and grabbed him and did CPR but it was too late."
Witness Michelle Campano, who is holidaying in Byron Bay, told the Daily Mail: "It was so horrible - we were swimming and got yelled out of the water. It took them 45 minutes to close the beach.
"I think the whole town is in shock."
Police Inspector Bobbie Cullen praised Mr Hickey, who risked his own life to retrieve Mr Wilcox. It was an "extraordinary act of bravery".
Mr Cullen said the victim's wife was at the beach when the tragedy occurred.
After the attack, lifeguards spotted a shark, believed to be a great white, just off the beach.
Mr Cullen said lifeguards used a helicopter and jet skis to try to push the shark out to sea. He said there was no plan to kill the shark, noting that great whites are protected.
The victim was brought on to the beach but was thought to have died from blood loss in the water.
NSW Ambulance paramedic Andrew Chapman said Mr Wilcox was bitten above the knee. "It was a fatal bite with major blood loss. He probably died in the water because there was no blood loss on the beach."
Local resident Ronny Monks, a member of the Byron Bay Surf Lifesaving Club, said the attack was a shock.
He said he swam the same stretch of water every day and despite the water being cold and murky in recent times he never thought such a big shark would come so close to the shore.
"I've heard of a couple, but never seen any," he said.
"It's normally safe as a bank here. It's so tragic."