Spinels (AB2O4) with magnetic ions occupying only the octahedral B sites have inherent magnetic frustration which inhibits long-range magnetic order (LRO) but may lead to exotic states. Here we report on the magnetic properties of the tetragonal spinel Zn0.8Cu0.2FeMnO4, the tetragonality resulting from Jahn-Teller active Mn3+ ions. Analysis of the temperature dependence of magnetization (M), heat capacity Cp, and neutron diffraction measurements show complex temperature-dependent short-range ordering (SRO) but without LRO with spin arrangement (Cu2+ ↓)A[Fe2+ ↑, Fe3+ ↓, Mn3+ ↑]B leading to FM clusters interact antiferromagnetically (AFM) at low-T. The relaxation time τ obtained from the Power law and Vogel-Fulcher laws confirm the cluster spin-glass state. The field dependence of spin-glass temperature TSG (H) follows the equation: TSG (H)=TSG(0)[1-AH(2/ϕ) ] with TSG (0) = 46.6 K, A = 8.6 ×10‒3 Oe‒0.593 and ϕ = 3.37. The temperature dependence of hysteresis loops yields coercivity HC ~ 3.8 kOe at 2 K without exchange-bias but HC decreases with increase in T and vanishes at 24 K, the TSG(H) for H = 800 Oe. Variations of Cp-T from 2 K to 200 K in H = 0 and H = 90 kOe do not show any peak characteristic of LRO. However, after correcting for the lattice contribution, a broad transition typically of SRO becomes evident at 40 K. For T < 9 K, Cp varies as T2; a typical signature of spin-liquids. Comparison of the neutron diffraction measurements at 1.7 K and 79.4 K shows absence of LRO. Time dependence of thermoremanent magnetization studies below 9 K reveal weakening of the inter-cluster interaction with increase in temperature. A summary of these results is that in Zn0.8Cu0.2FeMnO4, ferromagnetic clusters interact antiferromagnetically without LRO but producing a cluster spin-glass state at TSG(0) = 46.6 K, followed by spin-liquid behavior below 9 K.