Mirrors can be seen everywhere in daily life and play an important role in modern optical systems. A traditional mirror, which is made of noble metals, usually has a zero electric field strength and maximal magnetic field strength at its surface induced by the out-of-phase of electric field and in-of-phase of magnetic field between the reflected field and incident field due to the boundary condition of perfect electric conductor. As the magnitude of local electric field determines the strength of the light-matter interaction, it is clear that this interaction is suppressed near the mirror surface. Magnetic mirror, which can enhance electric field on the surface, has been widely applied to strong light-matter interaction for biological sensing, material analysis, and imaging. However, the conventional smooth magnetic mirror with a plane surface is difficult to induce sufficient light-matter interaction when the matter has a complex geometrical shape. Here in this work, we propose a concept of magnetic mirror with a rough interface designed by an array of artificial surface plasmonic structures. The artificial surface plasmonic structure on a subwavelength scale is designed by periodically inserting spiral metallic strips into a dielectric cylinder to support the strong magnetic dipolar resonant mode. The magnetic dipolar resonance of the excited structure is induced by the displacement current circle. Therefore, the resonant frequency is related to the geometrical parameters of the helical structure closely. When we reduce the outer radius of the structure, the magnitude of the displacement current circle will change, resulting in blue-shift of the resonant frequency. At the same time, we also find that increasing the spiral degree of the structure will cause the magnetic dipolar resonance frequency to become red-shifted. Particularly, the same magnetic dipolar mode can be supported in a spiral structure of different size by tuning the spiral degree accordingly. In this context, we design a rough magnetic mirror constructed by the artificial surface plasmonic structures with various sizes, and demonstrate that the efficiency of rough magnetic mirror is in agreement with that of smooth magnetic mirror. The proposed rough magnetic mirror can provide the unique ability to enhance the interaction between light and complicated matter for the application of biological sensing and imaging in microwave and terahertz band.