Can you breathe with a rubber dam in your mouth?

Yes: You will be able to breathe with a rubber dam on. The rubber dam will isolate the teeth that are being treated. This is important to insure a quality filling.

More importantly:: You generally can't breathe without a rubber dam during dental care. Without it, your mouth is full of water, saliva, cotton, suction tubes, bits of decayed tooth, old filling, etc. With it, the high volume suction takes it all away--no risk of choking, swallowing anything foreign. I almost never work without it. Much safer to work with it than not.

Of course: The rubber dam is used for two main reasons. First to isolate the tooth in order to maintain a more sterilized field & secondly to prevent debris, water, and materials to enter your mouth where you might swallow or aspirate them. There is plenty of room around the rubber dam to allow you to breath in and out. Even if that area were completely closed off you can breathe through your nose.