A.T. Robertson Commentary Acts 13:28

"And though they found no cause of death [in him], yet asked they of Pilate that he should be slain." — Acts 13:28 (ASV)

Though they found no cause of death (μηδεμιαν αιτιαν θανατου ευροντες). Second aorist active with usual negative of the participle. As a matter of fact the Sanhedrin did charge Jesus with blasphemy, but could not prove it (Matthew 26:65; Matthew 27:24; Luke 23:22). At this time no Gospel had probably been written, but Paul knew that Jesus was innocent. He uses this same idiom about his own innocence (Acts 28:18).

That he should be slain (αναιρεθηνα αυτον). First aorist passive infinitive, the accusative case, the direct object of ηιτησαντο (first aorist middle indicative, asked as a favour to themselves).