When "blunt" means direct and straightforward:
* Indirect
* Circumspect
* Subtle
* Tactful
* Diplomatic
* Polished
* Evasive
* Devious
When "blunt" means dull or not sharp:
* Sharp
* Pointed
* Keen
* Acute
* Fine
* Precise
When "blunt" means lacking in sensitivity:
* Sensitive
* Compassionate
* Empathetic
* Considerate
* Thoughtful
* Kind
To choose the best opposite, consider the specific meaning of "blunt" in the sentence you're using it in.