Magnetorheological elastomers (MREs) are composed of soft silicone rubber, carbonyl iron particles (CIPs), and various additives. This study designs and fabricates a novel hybrid-mode MRE isolator that can operate in both compression and shear modes simultaneously. Experimental and modeling investigations are conducted to examine the dynamic mechanical properties of the hybrid-mode MRE isolator under varying excitation frequencies, displacement amplitudes, and magnetic field strengths. The equivalent stiffness, energy dissipation, and equivalent damping of the MRE isolator are determined. Experimental results reveal that the hybrid-mode MRE isolator exhibits a pronounced MR effect by utilizing a hybrid magnetic field generation system, with all three parameters significantly increasing as the magnetic field strength increases. However, as the excitation frequency increases, the equivalent stiffness and energy dissipation increase, while the equivalent damping decreases. Based on the experimental findings, a compression–shear hybrid fractional-derivative parametric (CSHF) model is proposed to describe the impact of different operating conditions on the dynamic viscoelastic properties of the MRE isolator. A comparative analysis of the experimental results and model predictions indicates that the proposed mechanical model can accurately describe the dynamic mechanical characteristics of the hybrid-mode MRE isolator.