We have studied the T- and H-dependent magnetism in Mn(dca)₂(pyz) [dca = N(CN)₂^-, pyz = pyrazine] using neutron-scattering methods. The crystal structure can be viewed as a molecular analog of ReO₃, where 1D Mn-pyz-Mn chains connect 2D Mn(dca)₂ square sheets to form a 3D network. In zero field, the Mn²⁺ moments order antiferromagnetically below 2.53(2) K along the ac diagonal with a magnitude of 4.15(6) 7B at 1.35 K. The field-dependent response of the [111] magnetic reflection is consistent with spin-flop and induced ferromagnetic phase transitions as previously observed in magnetization measurements. Diffuse-scattering studies indicated no evidence for low-dimensional spin correlations. Using quasielastic neutron scattering, a low-energy spin-wave excitation was observed at ~0.23 meV, which is ~1/6 the momentum transfer observed in Mn(dca)₂ owing to a reduced number of magnetic nearest neighbors.