The second attack, which happened this afternoon, occured just kilometres away from an earlier incident this morning.
The wounded victim is a man in his thirties.
The 41-year-old was bitten on his right leg and his board left with visible teeth marks.
Surf photographer Peter Jovic saw the attack on Mr Travaglini and said everyone was "walking around like stunned mullets" afterwards. Credit: ABC Breakfast radio.
Friends used rope from his board as a tourniquet and provided first aid until emergency crews arrived from Margaret River within six minutes, a St John Ambulance spokesman told AAP.
He is conscious and breathing and is being taken to the Royal Perth Hospital by RAC Rescue.
"The surfer who was being attacked ended up miraculously body surfing into a little wave and getting pushed in by a local at the same time, who was out there with him, and making it to shore before everyone came to his aid", Jovic added.
Another witness, Brett Newland, said there were about five surfers in the area when "a big shark popped up in the water amongst them".
Surf Life Saving WA said a shark was spotted at Cobblestones surfing spot.
Volunteer fire crews are on the beach to assist the helicopter in landing.
"It is possible the decomposing carcass will continue to act as an attractant that could lead to sharks coming close in to shore along this stretch of coast", a statement said.
The Margaret River Pro worldwide surfing competition which is taking place nearby has been put on hold while organisers wait for information from local authorities.
Opposition Leader Mike Nahan said the attack would make global news because of the Pro event.
"The current policies are simply not adequate".