It is difficult to alter the thermal performance of a minichannel heat sink with a fixed structure under constant operating conditions. In particular, if the local heat transfer of the substrate cannot be regulated in real time, the dynamic heat dissipation needs of high-power electronic components cannot be met in the electrical servo systems of flight vehicles. In this paper, a new minichannel heat sink structure based on the classical rectangular channel is proposed and a piezoelectric oscillating fin (POF) is introduced to replace the fixed fin. The thermal performance of the heat sink can then be regulated using the swing of the POF, with supercritical carbon dioxide (S–CO2) as the coolant. Transient numerical simulations are applied to investigate the influence of various POF operating parameters on the heat transfer of the channel, such as the oscillation amplitude and frequency. The results demonstrate that a channel with a POF can allow for dynamic and rapid adjustment of the thermal performance through control of the oscillation frequency and amplitude of the POF, with a constant channel configuration, coolant, and operating conditions. The heat transfer can be enhanced significantly by the swing of the POF, with the local Nusselt number growing up to 8.3 times and the overall one up to 1.14 times. Both the oscillation frequency and amplitude have a positive correlation with the intensity of heat transfer. The POF also contributes to a greater pressure drop and fluctuation in pumping power. A comprehensive evaluation coefficient shows that the POF is effective at improving the overall thermal performance with a low-frequency swing, while high-frequency operation enhances the local heat transfer and decreases the local temperature near the tail end of the POF. Finally, considering the effects of the frequency and amplitude of the POF, as well as the variable thermophysical properties of the supercritical coolant, a heat transfer correlation based on the Dittus–Boelter equation is established to predict the thermal performance of the channel with a POF. This prediction has a maximum error of ±0.56%.