Auger mining (AM) is an effective and safe way to excavate an extremely thin protective layer. This method can relieve pressure and enhance the permeability of an ultra-contiguous coal layer with high gas capacity. However, there have been few studies on AM. Based on the conditions of a coal mine in Shanxi Province, China, theoretical analyses, laboratory tests and numerical simulations were used to analyze the evolution law of the overburden permeability in an AM face. A stress–damage–permeability coupling model was proposed, and a numerical simulation algorithm for fluid–solid coupling with FLAC software was established. Through this method, the evolution law of stress and permeability and its influencing factors of the overburden of the AM face were found. The intermediate coal pillar (ICP) width and the AM height and length are the main factors influencing the permeability evolution of the AM face. The first factor determines the damage state of the ICP in the goaf, and the last two factors influence the zone size with permeability enhancement of the protected layer. Therefore, reasonable AM parameter design is the key to both safe mining operations in the AM face and pressure relief and permeability enhancement.