It sounds like your dog need some training...

Maybe it's too tired to get above or under the door- you didn't mention where on it's body are the cuts.

anyway, i think the first thing to do is to cover the edges of the door with cloth or a towel in order to make it softer for him- that way it won't heart your dog.

Besides, if your dog is not very old, you can try and teach him how to get safely thru the door- by simple training with a food it likes.

good luck!

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