The effect of the cationic redistribution on the complex spinel structure and magnetic properties were investigated in Zn0.7Cu0.3Fe2O4 ferrite. X-ray photoelectron spectroscopy and x-ray diffraction studies revealed that the system exhibits a mixed spinel structure with Fe3+, Zn2+, and Cu2+ occupying both tetrahedral and octahedral sublattices. The DC magnetization results revealed the absence of long-range magnetic order in the system. Furthermore, the AC susceptibility data analysis using dynamic scaling laws suggests that the system exhibits magnetic relaxation below two different temperatures: (i) a spin-glass-like transition at low temperature (-49.2 K) with critical exponent 10.3 and spin-flip time -10-11 s, and (ii) a cluster-glass-like transition at higher temperature (-317 K) with critical exponent 4.6 and spin-flip time -10-10 s. The existence of glassy behavior and magnetic memory effects below the spin-glass transition temperature proves that the system is in nonequilibrium dynamical state. The coexistence of spin-glass and cluster-glass along with the thermal hysteresis between these two transitions could widen the technological applications of these systems.