In this work, we present four types of topological bicontinuous porous structures, namely Gyroid (G), Schwarz Diamond (D), Schwarz Primitive (P), and iWp (W), which are generated from mathematically defined triply periodic minimal surfaces. A systematic semi-theoretical investigation is performed to analyze the relations between the microstructures and the macroscopic mechanical behavior. Benefiting from the straightforward controllability on parameters, the scaling laws of the geometrical properties and mechanical properties are determined as functions of the relative density according to numerical analysis and computational simulation. An application to additive manufacturing accompanying with uniaxial compression testing is also performed, and the results show a highly agreement with the above scaling laws. Moreover, the simulation results indicate that the mechanical properties are highly dependent on topological architectures, which affect the deformation behavior of porous materials. It is shown that P topology has the highest stiffness and strength with stretching-dominated mode, while the rest exhibit a flexibly bending-dominated deformation behavior. The present study provides not only new insights into the structure-property relations of such topologies, but also a practical guide for their fabrication and application.