A diver has been killed by a large shark off the west Australian coast in the country's second fatal attack in less than a week.

Western Australia state police say the 60-year-old woman was diving with a man at a popular spot in the northern Perth suburb of Mindarie on Sunday when the shark attacked.

Police Inspector Danny Mulligan said the woman's dive partner managed to pull her out of the water after she was attacked, but her injuries proved fatal.

The woman was the second person killed by a shark in Western Australia in less than a week.

On Tuesday, a surfer's leg was bitten off by a shark about 60 miles south of where the woman was attacked. The surfer, Ben Gerring, later died of his injuries.

The brother of 29-year-old Mr Gerring thanked the "heroes" who took him to shore after the attack, and the staff at Royal Perth Hospital, where he died on Friday night.

Rick Gerring said the hospital's care had given the family three days with Ben.

"Obviously we were always hoping for the best outcome, it was always at the back of our minds that this could happen, but they gave us that time to say our goodbyes," he told ABC News.

Mr Gerring was attacked while paddling his surfboard at Falcon Beach in his home town of Mandurah, south of Perth.

Fellow surfers paddled to him to take him to shore, witnesses said.

An inspection of his damaged surfboard showed a white shark was responsible. The Fisheries Department trapped and killed a large shark on Wednesday afternoon but did not know if it was the same shark that attacked Mr Gerring.

Area beaches have reopened, but the department warned people to be extra cautious in the water.