What did Saul think he was accomplishing when he persecuted believers?

Saul of Tarsus believed he was doing God's service by trying to stamp out the early Jewish believers who confessed Jesus as the Messiah. His persecution stemmed from religious convictions, not a charge of blasphemy, as he thought he was defending God's honor.

Les explains that Saul of Tarsus was a Jew, a Pharisee of the Pharisees, who hated the very name of Jesus of Nazareth. His opposition was not because he thought Jesus was a blasphemer per se, but because of his religious convictions. Saul honestly thought he was doing God's service by trying to stamp out the early Jewish believers who held that Christ was the Messiah. This occurred in the transitional book of Acts, after the stoning of Stephen, at whose feet the witnesses laid their cloaks. Saul's zeal was a misguided attempt to serve God according to his Pharisaic convictions.

What did Saul of Tarsus think he was accomplishing by persecuting believers?

Saul of Tarsus thought he was doing God's service by trying to stamp out the early Jewish believers who held that Christ was the Messiah. His motive was religious conviction, not a charge that Jesus was a blasphemer, and he believed his persecution was faithful service to God.