prognati

1. to exile; to banish; to expel
   Režim je prognao mnoge pisce iz zemlje. — The regime exiled many writers from the country.
   Hiljade ljudi su prognane iz svojih domova. — Thousands of people were driven from their homes.
2. (of thoughts, feelings) to banish; to drive away
   Prognao je sve sumnje iz glave. — He banished all doubts from his mind.

The imperfective is progoniti, which more often means "to persecute, to pursue".