If you banish someone from society, you've caused that person's ostracism. Quakers, for example, faced ostracism by Puritans in colonial Massachusetts and many of them fled to the nearby colony of Rhode Island.
Ostracism comes from the Greek word ostrakon, a broken shard of pottery. Athenians used pieces of pottery as a paper substitute in an annual vote in which citizens chose to banish someone from Athens for a period of ten years. The banished person had to leave (or face death) but was allowed to keep his property and could return when his ostracism was up. The vote was often used to get rid of potential tyrants and political rivals.