To clarify the anomalous corrosion behavior in Cu-containing CoCrNi-based medium-entropy alloys, in which an enhanced corrosion driving force is accompanied by a reduced overall corrosion rate, the phase constitution, microstructure, electrochemical behavior, post-corrosion morphology, and surface chemical states of CoCrNi, CoCrNiCu, and CoCrNiCuFe alloys were systematically compared. The results show that Cu addition induces pronounced phase separation in the CoCrNi matrix, leading to the formation of a Cu-depleted FCC1 phase, a continuous Cu-rich FCC2 intergranular network, and dispersed nanoscale Cu-rich precipitates, with an FCC2 area fraction of about 0.145. In 3.5 wt.% NaCl solution, CoCrNiCu exhibits a stronger thermodynamic tendency for corrosion, whereas its overall corrosion rate does not increase, but instead shows the lowest corrosion current density and higher impedance, indicating an anomalous electrochemical response. Post-corrosion SEM morphology, EDS elemental mapping, and XPS valence-state analyses further reveal that corrosion is mainly concentrated in the Cu-rich phases and their adjacent narrow regions, while the Cu-rich phases themselves remain relatively stable as non-sacrificial cathodes. Semi-quantitative thermodynamic and mass-transport calculations indicate that although Cu-induced phase separation enhances the micro-galvanic corrosion driving force, with an estimated interphase potential difference of about 0.337 V, the overall corrosion rate remains constrained by the oxygen diffusion supply during cathodic oxygen reduction on the Cu-rich regions. Therefore, the anomalous corrosion response of CoCrNiCu can be attributed to the synergistic effect of the enhanced micro-galvanic corrosion driving force caused by Cu-induced phase separation and the restricted cathodic oxygen supply.