How did dionysus kill perseus?

Dionysus did not kill Perseus.

The only reference to Perseus' death is a very obscure legend recounted by Hyginus.

Pseudo-Hyginus, Fabulae 244 (trans. Grant) (Roman mythographer C2nd A.D.) :

"Men who killed their relatives . . . Megapenthes, son of Proetus, killed Perseus, son of Jove [Zeus] and Danae on account of the death of his father."

Proetus had been King of Argo and was great-uncle of Perseus; Megapenthes was also a King of Argos.