The Greek ekdiōkō is an intensified form of diōkō (to pursue/persecute), with the prefix ek indicating thoroughness or completion. It means to drive out completely, to persecute with the intent of total expulsion. In Luke 11:49, Jesus prophesies that some of God's messengers will be killed and others ekdiōkō — persecuted and expelled. Paul uses it in 1 Thessalonians 2:15 describing those who killed Jesus and persecuted the apostles.
The escalating intensity of ekdiōkō — total, driving-out persecution — reflects the reality that the gospel has always provoked violent opposition from those whose power it threatens. Paul describes this in his own experience (Galatians 1:13; 1 Corinthians 15:9) — he himself was once the one doing the ekdiōkō before the Damascus encounter transformed him. The church's suffering through persecution has historically been the very means by which the gospel spreads — the scattered become missionaries (Acts 8:1,4).