WHITE SULPHUR SPRINGS, West Virginia, July 6, 2012 (AFP) -
Simpson birdied the par-three 18th on the par-70 Old White TPC course to complete a bogey-free four-under 66 for nine-under 131.
He broke out of a logjam atop the leaderboard, with Jonathan Byrd, Charlie Beljan, Jeff Maggert and Jerry Kelly all in the clubhouse on eight-under 132 as the round was winding down.
But 14-time major champion Woods and Mickelson finished their rounds outside the projected cut line of one-under 139.
Mickelson, who played in the morning, posted his second-straight one-over 71 for 142.
Woods, playing alongside Simpson, started the day one-over and was even par with one bogey and one birdie through seven holes when thunderstorms halted play.
When play resumed, Woods completed a one-under 69, capping it with a birdie at 18 that still left him on even-par 140 and one shot outside the projected cut.
"I didn't quite have it," Woods said.
Woods, who missed the cut at Quail Hollow this season, has missed two cuts in one year just once before as a professional -- in 2005 when he missed the cut at the Byron Nelson Championship and the FUNAI Classic at Walt Disney World Resort.
Woods came into the event fresh off his 74th career victory at the National.
That made him the season's only three-time winner on the US tour. He took titles at the Memorial in June and the Arnold Palmer Invitational in March, although he was unable to build on those successes at the Masters or US Open.