Focal research has been conducted on medium-entropy alloys (MEAs) that exhibit a balanced combination of strength and plasticity. In this study, the microstructure, dynamic mechanical properties, and texture evolution of an as-cast medium-entropy CoCr0.4NiSi0.3 alloy were investigated through dynamic compression tests at strain rates ranging from 2100 to 5100 s−1 using the Split Hopkinson Pressure Bar in order to elucidate the underlying dynamic deformation mechanism. The results revealed a significant strain rate effect with dynamic compressive yield strengths of 811 MPa at 2100 s−1, 849 MPa at 3000 s−1, 919 MPa at 3900 s−1, and 942 MPa at 5100 s−1. Grains were dynamically refined from 19.73 to 3.35 μm with increasing strain rates. The correlation between adiabatic temperature rise induced by dynamic compression and dynamic recrystallization was examined, revealing that the latter is not associated with adiabatic heating but rather with phase transition triggered by the dynamic stress during compression. The proportion of Σ3n (1 ≤ n ≤ 3) grain boundaries in deformation specimens increases with increasing strain rates during dynamic compression. The formation of specific three-node structures enhances both strength and plasticity by impeding crack propagation and resisting higher mechanical stress. In the as-cast state, significant anisotropy was observed in the MEA. As strain rates increased, it transited into a stable {111}<112> F texture. The exceptional dynamic properties of strength and plasticity observed in the as-cast state of the MEA can be attributed to a deformation mechanism involving a transition from dislocation slip to the formation of intricate arrangements, accompanied by interactions encompassing deformation nanotwins, stacking faults, Lomer–Cottrell locks, stair-rods, and displacive phase transformations at elevated strain rates.