General:
* Strike
* Hit
* Bash
* Wallop
* Thump
* Beat
* Pummel
* Slam
* Crush
* Destroy
More specific:
* Punish: If you're using "smite" in a sense of divine punishment, you could use "chastise," "rebuke," or "afflict."
* Cut down: If you're using "smite" to mean "kill," you could use "slay," "fell," "execute," or "destroy."
* Affect: If you're using "smite" to mean "have a strong impact on," you could use "afflict," "devastate," or "overwhelm."
The best synonym for "smite" will depend on the specific situation and the intended meaning.