Spin glasses (SGs), generally defined as disordered systems with randomized competing interactions, are widely investigated complex phenomena. Discovering the ground states of spin glasses is crucial for understanding the nature of disordered magnets and many other physical manifestations, while also helping to solve some hard combinatorial optimization problems across multiple disciplines. However, the intrinsic cause of SG has always been elusive, especially in spinel oxide systems. Herein, we report the SG behavior observed in the cubic spinel oxides CoCrGaO₄, and provide a comprehensive understanding of its intrinsic source. Magnetic results indicate a frustrated state under multi-magnetic competition, and the features of SG are confirmed by susceptibility tests. The fitting parameters of $\tau$₀, T₀, and zv of isothermal remanent magnetization further reveal the relaxation behavior and strong spin frustration. Furthermore, the varying exchange coupling under different temperatures and magnetic fields is unveiled, which should be responsible for the disordered state. Our studies unravel the underlying mechanism responsible for doping-induced magnetic frustration and introduce CoCrGaO₄ as a potential platform for investigating spin glass behavior, thereby advancing fundamental research on frustrated magnetism within the spinel system.