Simpson, 36, was training to serve as the strategist for Artemis Racing in the Cup, the high-speed regatta that takes place from July to September.
Teammates pulled Simpson from the wreck shortly after 1 p.m., Coast Guard officials said. He was rushed to shore, where 20 frantic minutes of CPR failed to revive him, the San Francisco Chronicle reported.
Authorities said the other 10 sailors had also been thrown in the water, but had been able to drag themselves into the support boats nearby.
"We obviously had a tragic day out on the bay," said Paul Cayard, a six-time America's Cup veteran and CEO of the Artemis team, sponsored by the Royal Swedish Yacht Club. "Our thoughts and prayers are with the Simpson family, his wife and kids and the rest of the team. This was a shocking experience to go through. We have a lot to deal with in the next few days to ensure everyone is well."
The 72-foot catamarans used by America's Cup crews can reach up to 46 mph, transforming the sport into an extreme and often dangerous pursuit.
The great hight of the sail -- 131 feet -- makes the boats susceptible to capsizing if not maneuvered deftly in high winds.
"You always have to pay attention to the wind," said Coast Guard auxiliary member Bart Rugo, who described Thursday's winds as "a little above normal." "If you don't make a turn at the right time with a boat like that, it's easy to go over. With that much sail, the margin of error is small."
In October, an Oracle Team USA sailboat overturned, tossing its 11-man crew into the water of San Francisco Bay. The boat was destroyed when the tide smashed it against the Golden Gate Bridge, but none of the sailors was seriously hurt.
Simpson's is just the second death in the Cup's 162-year-history. His 30-year sailing career was capped by triumph: a gold medal at the 2008 Beijing Olympics and silver in London last year.
Your heart just sinks," said Bob Naber, commodore with the Bay Area Multihull Association. "This was a spectacular young man. A two-time medal winner and a father. ... There's just a big sadness."
Press conference video:
Arial footage of the wreck's aftermath: