As the power of electric vehicles (EVs), lithium-ion batteries (LIBs) are subjected to a variety of mechanical loads during electrochemical operation. Under this operating environment, lithium-ion batteries are at risk of internal short circuit, thermal runaway and even fire, threatening the safety of electric vehicles. The purpose of this paper is to investigate the mechanical behaviors and failure mechanisms of the battery separator to improve the safety of lithium-ion batteries under mechanical loads. In this study, uniaxial tensile, through-thickness compression and biaxial punch tests were performed to characterize two types of separators, dry-processed polypropylene (PP) separators and wet-processed ceramic-coated separators, and to analyze and compare their mechanical properties and failure modes. The comprehensive mechanical tests show that the failure modes of the different separator types are different, with the more anisotropic separator having more complex failure modes. Wet-processed ceramic-coated separators form localized and relatively more elliptical failure fractures, which may lead to larger short-circuit areas, while failure of dry PP separators leads to slit on machine direction. Finally, based on the uniaxial test data, developed a finite element model for dry-processed PP diaphragms in LS Dyna, which successfully predicted the response of dry-processed PP separators under biaxial tests.