Flexible microporous metal rubber (FMP-MR) is a high-damping material that dissipates energy by dry friction through internal spiral metal wires in contact with each other. However, the FMP-MR energy dissipation mechanism is not fully understood owing to its disordered grid interpenetrating structure. In this work, computer-aided preparation technology is used to accurately reconstruct the complex spiral network structure of FMP-MR multipoint random contact, and a cell group model with an energy dissipation mechanism is proposed to obtain the dynamic energy distribution of the contact friction in both space and time dimensions. By judging the effective contact point, a global displacement ablation phenomenon of hooked staggered porous materials is induced. The macro- and micro-equivalent frictions are introduced to effectively explain the characteristics of the strong energy dissipation in FMP-MR under fretting excitation. A real and effective damping hysteresis constitutive model is then constructed to dynamically capture the mapping relationship between the complex nonlinear topological structure effect of the materials and spatial random contact dry friction in real time. The results indicate that the contact behavior between turns of the FMP-MR wire follows a clear quasi-Gaussian distribution under an external load, forcing the topological results to change. The energy dissipation of the materials revealed peak energy consumption lagging behind the loading limit for a certain distance, which can be determined by the effective contact point and contact dry friction slip. The consistency between the quasi-static compression tests and constitutive curves of the model was quantitatively verified through residual analysis. The data demonstrated the differential behavior of the FMP-MR meso-structure to follow a phased growth law during loading with different action mechanisms in the guiding, main growth, and relaxation stages of the energy consumption displacement curve. In summary, these findings provide an acceptable theoretical basis for the damping energy consumption mechanism and lifetime prediction of FMP-MR.