Most small animals love to chew on cardboard. There is always a risk that he is swallowing some if it, but if chewed properly in low quantities this does not pose a health hazard. Is he using the chewed pieces for bedding material?

If so, maybe he needs more ready-to-use bedding? You can buy bedding material from pet shops which are safe for consumption, and replacing the cardboard with this may be a good idea just in case he is eating any.