General:
* Eject
* Evict
* Discharge
* Remove
* Oust
* Banish
* Deport
* Expunge (remove completely)
For people:
* Dismiss (from a job or school)
* Exclude
* Relegate
For substances:
* Emit
* Excrete
* Discharge
* Erupt (for a volcano)
For air or gas:
* Exhaust
* Vent
For specific situations:
* Expel (from a country)
* Suspend (from school)
* Terminate (a contract)
The best synonym depends on the specific situation and the intended meaning.