This study presents a comprehensive first-principles investigation of and , focusing on their thermodynamic stability and mechanical behavior. The results reveal that, at absolute zero, Hf-rich with , is thermodynamically stable, whereas Y-rich with and with are unstable against decomposition into relevant competing phases, i.e., solid solution and for Y-rich and , and -rhombohedral B for . However, near-stability of Y-rich , where , with formation energies within 4 meV per atom above the Hf-Y-B convex hull implies its potential entropy-driven thermodynamic stabilization at elevated temperatures. Both and are mechanically stable, according to the Born stability criteria, and Vegard's law is largely obeyed for their structural parameters and elastic moduli. Hf-rich exhibits superhard behavior with a maximum Vickers hardness of 43.9 GPa at = 0.167, while that of ranges between 33 and 39 GPa and peaks at 38.2 GPa for = 0.875. The maximum Vickers hardness values of and surpass those of their constituent compounds. These findings offer fundamental insights into stabilities and mechanical performance of the - and - mixtures, providing theoretical guidance for future development of advanced metal boride-based hard-coating materials.