General:
* Eject
* Evict
* Discharge
* Remove
* Oust
* Banish
* Deport
* Expunge (for removing something from a record)
Specific:
* Excrete (for waste products from the body)
* Erupt (for a volcano)
* Emit (for gases or light)
* Exhale (for air from the lungs)
Informal:
* Kick out
* Throw out
* Boot out
The best synonym will depend on the specific context of your sentence.