Stewart had inherited pole on Friday after qualifying was cancelled due to rain.
On Saturday's morning session, when he was completing his second lap of the day, he got loose at the exit of turn two, hit the wall and damaged the right side and rear end of his car.
"I just... I screwed up," explained Stewart. "I got in too deep and got loose and couldn't save it."
Stewart, who earlier this year lost pole position in similar fashion at the same track but then went on to win the race on Sunday, added: "I know we can do it. I tore up a really good race car today."
The points leader rejoined the second practice in his back-up car, finishing 21st fastest, while on the final session he was 26th. The car he will now run on Sunday's event was last raced at Darlington Raceway, where he finished third.
Although Stewart will be forced to start form the back of the field due to switching to his spare car, he still has the strategic advantage of having the first pit box, something that proved helpful when he won at Pocono after starting from the rear as well back in June.
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