World number four McIlroy posted a two-over 74 in the first round and, though he improved on day two, a one-under 71 was not enough to see him into the weekend.
It marks the second straight missed cut for McIlroy, who suffered the same fate at the Irish Open, and his third in four events as he continues to struggle in a year blighted by injury problems.
He made the turn in 33 after birdies at the third, fourth and seventh, but he was unable to recover ground after he doubled the 13th for the second time in as many days and will go into next week’s Open in a very poor run of form.
Knappe, meanwhile, produced a stunning display to match the best round of the week and surge into contention at nine under.
The German started at the tenth and did not have to wait long for his first birdie - which came at the 12th - before he holed from the fairway for an eagle at 13.
He made gains at the next three holes to turn in 30 and bounced back from bogeys at the second and fourth with birdies on five, seven and nine to claim a share of the lead.
The Open will see Harrington return to Royal Birkdale, where he won his second Claret Jug, and he may do so on the back of a win if he can maintain his consistent form at Dundonald Links.
After a 67 on day one, Harrington posted a blemish-free 68 to bolster his hopes of a 16th European Tour success. Shinkwin matched his round but would hold the outright lead if not for bogeys at four and 15.
Ian Poulter and Andrew Dodt are a shot behind after 69s, with Rickie Fowler, Gregory Havret and Nicolas Colsaerts two strokes off the pace.
Matt Kuchar and Alexander Levy are six under, one ahead of overnight leader Mikko Ilonen, who went two over for the day.
Defending Open champion Henrik Stenson made the cut as he improved on his level-par round from Thursday with a 69, but Patrick Reed’s 70 was not enough for the American to scrape into the weekend.
Stenson’s Swedish compatriot Alex Noren also missed out, the world number nine posting a 76 to drop to slump to two over.
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