It could be argued that Giovanni does not love Beatrice at all. Giovanni does not love and accept Beatrice as she is; he cannot look beyond the poisonous elements in her physical nature in order to recognize and embrace the goodness beyond. Moreover, he not only fails to accept her, he cruelly condemns and rejects an essential part of her being. He does not believe that Beatrice is worthy of his love unless a significant part of her is destroyed.
Giovanni loves the Beatrice he wants her to be, and he will live with her only outside the garden, her sustaining environment. Giovanni's blind selfishness is his defining characteristic.
Beatrice drinks the antidote to her poisonous nature at Giovanni's request, knowing that it will end her life. Her motivation for doing this could be interpreted in this way; she chose to die rather than live without Giovanni. However, it could be interpreted another way, a more significant one. Having loved him so deeply, Beatrice could not bear the disillusionment in realizing that it was Giovanni who was not worthy of love. Unlike Beatrice, his poisonous nature encompassed not only his body, but also his spirit.