Graphene, an allotrope of carbon, has demonstrated exceptional mechanical, thermal, electronic, and optical properties. Complementary to such innate properties, structural modification through chemical functionalization or defect engineering can significantly enhance the properties and functionality of graphene and its derivatives. Hence, understanding structure-property relationships in graphene-based metamaterials has garnered much attention in recent years. In this thesis, we present molecular dynamics studies aimed at elucidating structure-property relationships that govern the thermomechanical response of interlayer-bonded graphene bilayers. First, we present a systematic and thorough analysis of thermal transport in interlayer-bonded twisted bilayer graphene (IB-TBG). We find that the introduction of interlayer C-C bonds in these bilayer structures causes an abrupt drop in the in-plane thermal conductivity of pristine, non-interlayer-bonded bilayer graphene, while further increase in the interlayer C-C bond density (2D diamond fraction) leads to a monotonic increase in the in-plane thermal conductivity of the resulting superstructures approaching the high in-plane thermal conductivity of 2D diamond (diamane). We also find a similar trend in the in-plane thermal conductivity of interlayer-bonded graphene bilayers with randomly distributed individual interlayer C-C bonds (RD-IBGs) as a function of interlayer C-C bond density, but with the in-plane thermal conductivity of the IB-TBG 2D diamond superstructures consistently exceeding that of RD-IBGs at a given interlayer bond density. We analyze the simulation results employing effective medium and percolation theories and explain the predicted dependence of in-plane thermal conductivity on interlayer bond density on the basis of lattice distortions induced in the bilayer structures as a result of interlayer bonding. Our findings demonstrate that the in-plane thermal conductivity of IB-TBG 2D diamond superstructures and RD-IBGs can be precisely tuned by controlling interlayer C-C bond density with important implications for the thermal management applications of interlayer-bonded few-layer graphene derivatives. Secondly, we report results on the mechanical and structural response to shear deformation of nanodiamond superstructures in interlayer-bonded twisted bilayer graphene (IB-TBG) and interlayer-bonded graphene bilayers with randomly distributed individual interlayer C-C bonds (RD-IBGs). We find that IB-TBG nanodiamond superstructures subjected to shear deformation undergo a brittle-to-ductile transition (BDT) with increasing interlayer bond density (nanodiamond fraction). However, RD-IBG bilayer sheets upon shear deformation consistently undergo brittle failure without exhibiting a BDT. We identify, explain, and characterize in atomic-level detail the different failure mechanisms of the above bilayer structures. We also report the dependence of the mechanical properties, such as shear strength, crack initiation strain, toughness, and shear modulus, of these graphene bilayer sheets on their interlayer bond density and find that these properties differ significantly between IB-TBG nanodiamond superstructures and RD-IBG sheets. Our findings show that the mechanical properties of interlayer-bonded bilayer graphene sheets, including their ductility and the type of failure they undergo under shear deformation, can be systematically tailored by controlling interlayer bond density and distribution. These findings contribute significantly to our understanding of these 2D graphene-based materials as mechanical metamaterials.