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Magnetic properties of (Zn_0.15Cu_1.85)V₂O₇ have been investigated on powder and single crystal samples using magnetization and neutron scattering measurements. The nuclear structure of (Zn_0.15Cu_1.85)V₂O₇ resembles that of monoclinic β-Cu2V2O7. Based on DFT calculations [PRB 82, 144416 (2010)], the spin couplings of these systems were found to topologically form a 2D honeycomb spin network. Combined magnetic susceptibility and power neutron diffraction suggest that the spins are co-aligned antiparallel along the crystallographic c-axis. Quantum Monte Carlo simulations based on the proposed honeycomb model with the dominant 5^th and 6^th nearest-neighbor exchange interactions provide a good fit to the magnetic susceptibility data. Inelastic neutron scattering data show the absence of nonreciprocal magnons, which were observed in the cousin phase of the noncentrosymmetric magnet α-Cu2V2O7 [PRL 119, 047201 (2017)]. The disappearance of the nonreciprocal magnons in (Zn_0.15Cu_1.85)V₂O₇ and presumably β-Cu2V2O7 can be explained by the absence of the Dzyaloshinskii-Moriya interaction.  In addition, the magnon dispersion is consistent with the proposed honeycomb spin model.