Go into combat mode and hold Alt. You can use this to attack pretty much anything. Axes should strike wooden objects like chests and doors without losing durability. Everything else will damage a melee weapon's durability. You can cheese this with throwing weapons, or just punch it and then heal.

You said attacking the door doesn't do anything, so if that's what you're already doing then it might be a door that's impossible to bash.

PS Be prepared for people to be upset about breaking their stuff.