We report the slow spin dynamics of cluster spin-glass (SG) spinel Zn(Fe1-xRux)(2)O-4 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 (chi(ac)(f, T)) and the subsequent analysis using the empirical scaling laws such as: (a) Vogel-Fulcher law and (b) Power law reveal the presence of cluster SG state below the characteristic freezing temperature T-SG (17.77 K (x= 0.5) and 14 K (x= 0.75)). Relaxation dynamics of both the compositions follow the non-mean field de Almeida-Thouless (AT)-line approach (T-SG(H) = T-SG(0)(1 - AH(2/phi))), with an ideal value of phi = 3. Nevertheless, the analysis of temperature dependent high field dc-susceptibility, chi(hf) (2 kOe <= H-DC <= 20 kOe, T) provides evidence for Gabay-Toulouse type mixed-phase (coexistence of SG and ferrimagnetic (FiM)) behaviour. Further, in the case of Cu0.2Zn0.8FeRuO4 system, slowly fluctuating magnetic clusters persist even above the short-range FiM ordering temperature (T-FiM) and their volume fraction vanishes completely across similar to 6T(FiM). This particular feature of the dynamics has been very well supported by the time decay of the thermoremanent magnetization and heat-capacity studies. We employed the high temperature series expansion technique to determine the symmetric exchange coupling (J(S)) between the spins which yields J(S) = -3.02 x 10(-5) eV for Cu0.2Zn0.8FeRuO4 representing the dominant intra-sublattice ferromagnetic interactions due to the dilute incorporation of the JT active Cu2+ ions. However, the antiferromagnetic coupling is predominant in ZnFeRuO4 and Cu0.2Zn0.8Fe0.5Ru1.5O4 systems. Finally, we deduced the magnetic phase diagram in the H-DC - T plane using the characteristic parameters obtained from the field variations of both ac- and dc-magnetization measurements.