Motivated by recent successful synthesis of transition metal dinitride TiN2, the electronic structure and mechanical properties of the discovered TiN2 and other two family members (ZrN2 and HfN2) have been thus fully investigated by using first-principles calculations to explore the possibilities and provide guidance for future experimental efforts. The incompressible nature of these tetragonal TMN2 (TM = Ti, Zr, and Hf) compounds has been demonstrated by the calculated elastic moduli, originating from the strong N-N covalent bonds that connect the TMN8 units. However, as compared with traditional fcc transition metal mononitride (TMN), the TMN2 possess a larger elastic anisotropy may impose certain limitations on possible applications. Further mechanical strength calculations show that tetragonal TMN2 exhibits a strong resistance against (100)[010] shear deformation prevents the indenter from making a deep imprint, whereas the peak stress values (below 12 GPa) of TMN2 along shear directions are much lower than those of TMN, showing their lower shear resistances than these known hard wear-resistant materials. The shear deformation of TMN2 at the atomic level during shear deformation can be attributed to the collapse of TMN8 units with breaking of TM-N bonds through the bonding evolution and electronic localization analyses.