Establishing the Time-Temperature and Frequency-Temperature Superposition Principles (TTSP and FTSP) to describe the mechanical behavior of polymeric materials is always of paramount significance. In this work, by adopting the classic coarse-grained model, we investigate the validity of these superposition principles for a series of networks, such as the pure polymer network, interpenetrating polymer networks composed of stiff and flexible networks (IPNs-SF), interpenetrating polymer networks composed of different cross-linking networks (IPNs-DC), polymer nanocomposites (PNCs), and surface grafted modified PNCs. The study focuses on the three critical mechanical properties such as the stress relaxation, the storage modulus versus the frequency obtained from the dynamic periodic shear deformation, and the uniaxial tensile stress-strain. The glass transition temperature (T) is about 0.47 for the simulated polymer network (CL400), and a smooth master curve is obtained for the stress relaxation process by setting the reference temperature T = 0.6 via the horizontal shifting process, indicating the validity of TTSP. Furthermore, similar smooth master curves are also achieved for both dynamic periodic shear and uniaxial tensile deformation, which exhibit similar trends and share the identical linear viscoelastic regime in the temperature interval above T: 0.55