How does Beatrice die in Rappaccini's Daughter?
Beatrice is poisoned -- sort of. Her father, a "mad scientist", conducts experiments on plants and flowers, trying to grow the most exotic and beautiful ones he can. His botany experiments are poisonous, however. Rappaccini also experiments on his daughter, Beatrice, giving her poisons as well, but to improve her, to make it so she can kill someone just by breathing on them, among other things. Rappaccini gives the same poisons to Giovanni, Beatrice's boyfriend, in an attempt to make him become like her and not succumb to the poison. When Giovanni tells Beatrice what her father has done, she swallows the antidote, but because she is so infused with the poisons, the antidote winds up killing her.
Read about it here on eNotes.