Structurally tailored and engineered macromolecular (STEM) gels are polymer networks containing latent initiator sites available for post synthesis modifications, with the networks acting as a backbone grafted with secondary polymer side chains. Here we use dissipative particle dynamics (DPD) simulations to study the mechanical response of the modified STEM gels under compression. We observe lower compressional modulus of the networks after adding secondary side chains and the mechanical properties are tunable by varying the grafting density and side chain length. To gain insight into the microscopic origin of observed mechanical behaviors, we measure the chain entanglements density, conformational entropy change, and conduct 3D structural domain analysis during the compression process. Furthermore, we show that attaching the initiator sites to the primary networks through labile links allows the links to break/rearrange, and thus relieves local stress concentrations.