General synonyms:
* Discourage
* Dishearten
* Depress
* Sap
* Undermine
* Break the spirit of
* Dampen
* Crush
* Disillusion
More specific synonyms:
* Discredit (if referring to reputation)
* Disrupt (if referring to plans or operations)
* Unnerve (if referring to causing anxiety)
* Degrade (if referring to lowering someone's status)
The best synonym will depend on the specific situation you are describing.