With the development of engineering technology and materials science, pure elastic materials can no longer meet the application needs of materials in industrial manufacturing. Magneto-electro-elastic (MEE) materials have more complex internal structures compared to classical elastic materials, and the methods for solving mechanical and physical performance are more difficult compared to classical elastic materials. Therefore, the mode III fracture behavior of MEE materials with nano-defects (pores and cracks) is investigated in this study. Based on the Gurtin-Murdoch surface theory and conformal mapping theory, the mode III fracture properties of MEE materials containing an arbitrary-location through crack emanating from a nano-hole under anti-plane mechanical loading, in-plane electrical loading, and in-plane magnetic loading are studied. The accurate solution of the MEE field in the matrix is obtained using the MEE theory and the far-field loading conditions. Analytical expressions for the MEE field intensity factors of the tips at both ends of the through crack, assuming that the surface of nano-defects is magneto-electric impermeable, are given. The proposed method is validated through a comparison with existing research. The effects of crack location, crack interaction, and the application of multiple physical loads on the dimensionless MEE field strength factors are discussed. The results show that the dimensionless MEE field intensity factors exhibit a significant size effect. The surface effect of nano-defects on the MEE tip fields of the cracks is constrained by the crack location. The dimensionless MEE field intensity factors are significantly affected by the ratio of the through crack length to the applied MEE loads. The results obtained in this study provide a theoretical basis for the experiments and numerical simulations of the mode III fracture behavior of an arbitrary-location through crack emanating from a nano-hole in MEE materials.