Solid-state batteries with lithium metal anode have been accepted extensively as the competitive option to fulfill the upping requirement for safe and efficient energy devices. Nevertheless, its wide-ranging application has been impeded by the failure of solid-state electrolyte (SSE) induced by development of lithium (Li) filament. Based on the nature of polycrystalline ceramic SSE with varying grain size and boundary strength, the constitutive equation coupled with electrochemical kinetics was applied to picture the propagation of damage and corresponding disintegration caused by the development of Li filament. Based on the results, we found that the stress generated along with the growth of Li filament spreads away via the opening and sliding of grain boundary. Thus, damage occurs along grain boundaries, of which propagation behavior and damage level are controlled by grain size. Especially, over-refinement and under-refinement of grains of SSE can cause flocculent damage with inordinate damage degree and accelerate the failure time of SSE, respectively. On the other hand, the failure time is powerfully prolongated through strengthening the grain boundary of SSE. Eventually, grain size of 0.2 μm and tensile strength of grain boundary of 0.8-time-of-grain are posted as the threshold to realize the postponed failure of NASICON-based SSE. Inspiringly, electro-chemo-mechanical model in this contribution is generally applicable to other type of ceramic SSE to reveal the failure process and provide the design guideline, fostering the improvement of solid-state batteries.