We report the slow spin dynamics of cluster spin-glass spinel Zn(Fe1-xRux)2O4 by means of detailed dc-magnetization and ac-susceptibility studies combined with the heat capacity analysis. Two specific compositions (x = 0.5, 0.75) have been investigated in detail along with the substitution of Jahn-Teller (JT) active spin-1/2 Cu2+ ions at B-sites. Measurements based on the frequency and temperature dependence of ac-susceptibility (χac (f,T)) and the subsequent analysis using the empirical scaling laws such as: (i) Vogel-Fulcher law and (ii) Power-law reveal the presence of cluster spin-glass state below the characteristic freezing temperature TSG (17.77 K (x = 0.5) and 14 K (x=0.75)). Relaxation dynamics of both the compositions follows the non-mean field AT-line approach (TSG (H)=TSG (0)(1-AH2/ϕ), with ideal value of ϕ = 3. Nevertheless, the analysis of temperature dependent high field dc-susceptibility, χhf (2 kOe ≤ HDC ≤ 20 kOe, T) provides evidence for Gabay‒Toulouse type mixed-phase (coexistence of spin-glass and ferrimagnetic) behavior. Further, in case of Cu0.2Zn0.8FeRuO4 system, slowly fluctuating magnetic clusters persist even above the short-range ferrimagnetic ordering temperature (TFiM) and their volume fraction vanishes completely across ~ 6TFiM. This particular feature of the dynamics has been very well supported by the time decay of thermoremanent magnetization and heat-capacity studies. We employed the high temperature series expansion technique to determine the symmetric exchange coupling (JS) between the spins which yields JS = ‒3.02×10‒5 eV for Cu0.2Zn0.8FeRuO4 representing the dominant intra-sublattice FM interactions due to the dilute incorporation of the JT active Cu2+ ions. However, the AFM coupling is predominant in ZnFeRuO4 and Cu0.2Zn0.8Fe0.5Ru1.5O4 systems. Finally, we deduced the magnetic phase diagram in the HDC–T plane using the characteristic parameters obtained from the field variations of both ac- and dc-magnetization measurements.