Anne died (in real life aswell as the show) because basically Henry had had enough of her because she didn't give him the son he wanted, so he had to find reasons to get rid of her, so they "found" evidence of adultery, witchcraft and supposedly incest. Plus by this time Henry really wanted Jane Seymour

I am a histoury major at Tulane and can tell you by looking at the documents of the court which i have seen first hand that she did have incest with her brother and she practised Alchemy and Tarot Cards.