When subjected to excessive shear deformation, viscoelastic (VE) dampers may inevitably suffer from damage, due to their VE material layers with limited thickness. Under the circumstance, their stiffness and energy dissipation capabilities may deteriorate but not totally vanish. To estimate the seismic performance of viscoelastically damped structures, the beyond design and residual performances of damaged VE dampers are crucial to protect structures from severe failure during the following main shock or aftershocks. On the other hand, for new viscoelastically damped structures under the normal design earthquakes, neglecting the residual performance of damaged VE dampers may result in non-conservative design. Thus, this study aims to provide approaches to analytically characterize the beyond design and residual performances of damaged full-scale VE dampers. The analytical predictions based on simplified fractional derivative models are compared with the experimental results. The proposed models work well for the design performance of the intact full-scale VE dampers. Particularly, those can also reproduce the beyond design and residual performances of damaged full-scale VE dampers, if due consideration is taken of the effects of excitation frequencies, ambient temperatures, temperature rises, softening, and hardening. Since the test data are limited, the capability of the proposed models may need further verification through comparing the analytical predictions with more test data in the future. In addition, the experimental and analytical results discussed in this study may be only valid for the VE damper specimens (Type ISD111) manufactured by the Nippon Steel & Sumitomo Metal Corporation, which still needs further demonstration by testing other different VE dampers in the future.