It says in the card "remove any face up adventure card in any region" Can I remove dungeon cards also?

Dungeon and Highland are regions.

Tuomas85 said:

Yes, but you have to be inside the Dungeon for this effect to be applicable to Dungeon cards. Effects and Special Abilities involving Adventure cards apply to Dungeon cards when the Character is inside the Dungeon.

In the same fashion, you cannot use Destruction against Adventure cards on the main board while you're in the Dungeon Region.