John Calvin Commentary Acts 9:2

"and asked of him letters to Damascus unto the synagogues, that if he found any that were of the Way, whether men or women, he might bring them bound to Jerusalem." — Acts 9:2 (ASV)

And Luke also describes that Saul was equipped with weapons and power to do harm, for Luke says that Saul had obtained letters from the high priest, so that he could bring to Jerusalem, bound, all those he found professing the name of Christ. Mention is made of women, so that it might more clearly appear how eager he was to shed blood—he who had no respect for sex, whom even armed enemies are accustomed to spare in the heat of war. Therefore, Luke sets forth before us a fierce and cruel beast, who not only was given freedom to rage but also had his power increased to devour and destroy godly men, as if a madman had a sword put into his hand.

Although I have translated it as 'sect,' Luke uses way, a metaphor common enough in the Scriptures. Therefore, Paul’s purpose was to completely extinguish the name of Christ by cruelly destroying all the godly.