Brittle porous materials offer a wide variety of promising applications due to their high surface-area-to-volume ratios and controllable porous structures. Getting comprehensive knowledge of the structural stability is of great significance for avoiding the irreversible destruction of these materials. Based on interpenetrating bicontinuous structures, we innovatively adopted a sequential mesoscopic simulation strategy to show the pore size effect on the mechanical stability, which involves structural evolution by the mesoscale dynamic density functional method and mechanical behavior by the highly efficient lattice spring model. Simulation results show that specific surface areas, Young's moduli and fracture strains decrease with the increase of pore widths on the premise of the same porosity. More uniform stress/strain distributions are observed in structures with smaller pore sizes or more uniform defect distributions. From the local stress distribution analysis, the effective stress transfer occurs in the solid phase, which runs through the simulation box along the tensile direction, and the mechanical disparity among systems with different pore sizes is due to different volume fractions and microstructures of the solid phase. Larger pore sizes result in lower Weibull moduli due to the increased heterogeneity and a less predictable failure behavior, and the concentrated defects usually result in mechanical anisotropy.