Woods, the hottest player on the US circuit this season with three victories in his last seven events, struggled with distance control in his approach play on the way to a one-under-par 69 on the Old White TPC Course.
The 14-times Major champion needed to ace the par-three last to ensure he advanced to the weekend but his tee shot settled seven feet from the cup from where he sank the birdie putt for an even-par total of 140.
It will be only the ninth time Woods has missed the cut in a US Tour event as a professional, and the second occasion this year after his failure to progress at the Wells Fargo Championship in May.
"I didn't quite have it," a frustrated Woods said after mixing four birdies with three bogeys. "I drove it really good today and I just did not have the feel for distances.
"The ball was just going forever. I know we're at altitude but I just couldn't get the ball hit pin-high no matter what I did. And consequently I made some bogeys."
Woods, who overtook Jack Nicklaus in second place on the all-time list of US PGA Tour winners with his two-shot triumph at the AT&T National on Sunday, missed the cut in his next start after a victory for the third time in his career.
"It happens," the world number four said. "You miss cuts out here. I've been doing it for a long time (as a pro) and I've missed nine cuts. So one every couple of years, I guess."
Mickelson carded a second successive 71 to finish three strokes outside the projected cutline as he and Woods are poised to miss the cut in the same event for the first time since the 1993 Byron Nelson Championship.
"I don't know what to say about that," Mickelson said after a round including three birdies, two bogeys and a double-bogey at the par-three 15th. "The parts don't feel that far off, but I haven't been putting them together.
"I just don't get it," added the American left-hander, who also missed the cut here 12 months ago. "I certainly struggled a little bit on the greens both years, but nothing that should have led to these scores."
Play was suspended for just over two hours earlier on Friday due to the threat of lightning and the second round was eventually halted for the day in fading light with 12 players still out on the course.
While Mickelson and Woods were set to exit, fellow American Simpson carded a flawless four-birdie 66 to take control of the tournament with a nine-under total of 131 after 36 holes.
The 26-year-old, who clinched his first Major title by one shot in last month's US Open at the Olympic Club, knocked in a six-foot birdie putt on the 18th green to snatch the outright lead.
Compatriots Jonathan Byrd (68), US PGA Tour rookie Charlie Beljan (62), Jeff Maggert (68) and Jerry Kelly (66) were tied for second.
Simpson, who played with Woods for the first two rounds this week, needed no reminding by reporters that he led last year's Greenbrier Classic after 36 holes before falling back into a tie for ninth.
"I was confident last year, I'm confident this year," he said. "I don't think a whole lot has changed. I've learned a lot about myself in the final round since last year.
"But I've still got a long way to go, and there's a bunch of good players right there."
Eight-times Major champion Tom Watson, at the age of 62, birdied four of his first seven holes on Friday to shoot a 68 and will go into the weekend seven strokes off the lead.
The cut was projected to fall at one-under 139 with former Major winners Jim Furyk, Lucas Glover and Trevor Immelman also poised to miss out.