While there's no specific mention of how Dumbledore kills Grindelwald in the books, the movie "Fantastic Beasts: The Secrets of Dumbledore" portrays it as a duel where Dumbledore disarms Grindelwald and uses his own Elder Wand to deliver the killing blow.
It's important to note that the movie portrays this differently than the books, where the circumstances of Grindelwald's death are left more ambiguous.