Earthquakes contain complex components in both the horizontal and vertical directions. However, most vibration control strategies work only in a single direction. The existing multi-dimensional isolation devices usually have complex designs and low damping ratios; hence, the stability of structures that incorporate the devices is currently insufficient. This study designs a novel multi-dimensional isolation and mitigation device based on viscoelastic damping technology (VE-MDIMD). The device consists of a core bearing and several cylindrical dampers, providing vibration control capacity in both the horizontal and vertical directions and a strong uplift resistance. To evaluate the device’s performance, a series of dynamic tests are conducted on the cylindrical damper utilized in the device. The results show that the damper’s mechanical properties exhibit a pronounced dependence on the frequency and amplitude, and its hysteresis curves become obviously nonlinear with increased deformation. Subsequently, to describe the behavior of the VE-MDIMD, a mechanical model is established which combines the construction of the device and the characteristics of the damper. Considering the limitations of existing models in fully capturing the nonlinear behavior of the damper, a novel multi-scale model is proposed based on the microstructure of viscoelastic material. The experimental verification confirms that the model can accurately capture the frequency and amplitude dependence, as well as the nonlinear hysteresis behavior, of the damper. Finally, the effectiveness of the VE-MDIMD is evaluated through the dynamic analysis of an actual structure. The arrangement of the device in the structure is optimized based on a multi-objective genetic algorithm available in Matlab (R2019b) and OpenSEES (Version 3.0.0). The results demonstrate the device’s superiority in controlling both horizontal and vertical vibrations in the superstructure.