I'm betting the Mayor has plans of stopping Rou from being able to help Yuika, or even stop them from succeeding with their mission somehow, because he's a corrupt bastard that doesn't want to lose all the money he's been raking in with the dungeon still in operation.
Heck, I bet that the Mayor probably even knows full well what would happen if the dungeon doesn't get conquered, and plans on fleeing just in time to get out of there with all his treasures and valuables without getting caught in the blast, or whatever the Dungeon Core turns into after it reaches the limit.