Glover, another early finisher, carded a one-under 69 before increasing winds made afternoon play difficult.
Nine players were tied at four-under 136 on the tight leaderboard, including American Brooks Koepka (69) and Canada's Adam Svensson (64).
First-round leader Jhonattan Vegas stumbled to a three-over 73 that pushed him three strokes off the pace.
The Venezuelan had a two-shot advantage to start the day before two double-bogeys and a pair of bogeys derailed him.
Im made seven birdies and a lone bogey at the 16th.
“I was hitting the ball really well today, so all my putts were under 10 feet,” he told reporters.
Mitchell, who also has never won on the PGA Tour, played the back nine first, collecting five birdies and a bogey at the 17th.
“It’s definitely the (Bermuda) grass,” said Mitchell, who made all of his putts from inside 18 feet.
“I grew up on Bermuda. I know how to putt it. I know how to read it. It’s definitely helped a lot."
Defending champion Justin Thomas, nursing an injured right wrist after smashing his nine-iron into a tree when attempting a recovery shot on Thursday, squeezed into the weekend despite a four-over 74 featuring a triple and a double-bogey.
That put him right on the cut mark at two-over 142, but Australian former Masters champion Adam Scott missed out by a stroke.
American Gary Woodland and Canadian Drew Nesbitt also made the cut, with Nesbitt needing a little extra.
After finding water with a 308-yard drive on the sixth hole, Nesbitt removed his shirt before slapping his ball out of the hazard with his second shot to within 50 yards of the pin.
The lefthander then chipped to within four feet and saved par en route to a 71 that enabled him to make the cut at two-over 142.
Woodland made back-to-back birdie putts, including a 16-footer at the last, for an even-par 70 as he made his 21st consecutive cut at 142.
(Reporting by Gene Cherry in Raleigh, North Carolina, editing by Ed Osmond/Ian Ransom)
