When Albus and Severus discussed destroying Time-Turner, Albus suggested "stupefy", because "they were originally destroyed using Stupefy" (Part 2, Act 3, Scene 16)
But that seems to contradict JKR canon, since in HP&OotP, the Stupefy spell didn't destroy the Time-Turners. It didn't even hit them - it hit and destroyed the case where they were stored; and that cause the whole stock be stuck in an endless time loop:
Harry flung himself sideways as Neville took aim again and shouted, “STUPEFY !”
The jet of red light flew right over the Death Eater’s shoulder and hit a glass-fronted cabinet on the wall full of variously shaped hourglasses.
The cabinet fell to the floor and burst apart, glass flying everywhere, then sprang back up onto the wall, fully mended, then fell down again, and shattered —
Harry stuck his head out of the door and looked around cautiously. The baby-headed Death Eater was screaming and banging into things, toppling grandfather clocks and overturning desks, bawling and confused, while the glass cabinet that Harry now suspected had contained Time-Turners continued to fall, shatter, and repair itself on the wall behind them.
(OotP, CHAPTER THIRTY-FIVE - "BEYOND THE VEIL")
Of course, that kind of already got contradicted a bit in Half-Blood Prince, but the main point (they were shattered, not destroyed by "Stupefy") stands:
“We couldn’t have done,” said Hermione. “We smashed the entire stock of Ministry Time-Turners when we were there last summer. It was in the Daily Prophet.” (H-BP, CHAPTER ELEVEN - "HERMIONE’S HELPING HAND")