NASICON-type Na3V2(PO4)3 cathode materials can be regarded as promising candidates for high-power Na-ion batteries due to the observed facile kinetics of Na-ion de/intercalation. Substitution of V for Mn provides additional advantages related to the increase in the average operating potential and reduced cost of the active material. In this work, we explore the kinetics of Na+ intercalation into Mn-substituted Na3+xMnxV2-x(PO4)3 (x = 0, 0.1, 0.5, 1) materials with a primary focus on the impact of Mn content on the rate capability of the materials. We demonstrate that Mn substitution results in quite subtle changes in bulk ionic diffusivity and charge transfer rates, while more significant impact is observed on the nucleation kinetics, which induces large hysteresis between charge and discharge curves for Mn-rich materials. The increase in hysteresis between charge and discharge curves does not limit the specific energy retention at high C-rates significantly, yet the performance losses are mainly related to the slow phase boundary propagation for biphasic processes. The Mn-rich materials, which demonstrate wider single-phase regions, are shown to outperform the unsubstituted materials in terms of rate-capability and should be preferred for high-power applications.