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I'm not sure of the mailbox configuration, but I would wait until the dog was off the owners property if feasible.

I'm assuming you have talked to the dog owner and not gotten anywhere? You may also want to clearly document the situation through video combined with complaints to animal enforcement, etc., now. That way if the unfortunate situation occurs where you are forced to shoot the dog, you will have as much legal ammo as possible (pardon the pun).