Here "this Way" represents the people who belonged to the group called "the Way." Alternate translation: "I persecuted the people who belonged to this Way" (See: [[rc://en/ta/man/translate/figs-metonymy]])
The word "death" can be translated with the verb "kill" or "die." Alternate translation: "and I looked for ways to kill them" or "and I even caused them to die" (See: [[rc://en/ta/man/translate/figs-abstractnouns]])