As an important component, the properties of separators directly affect the capacity, life, and safety performance of lithium-ion batteries (LIBs). The high thermal stability and safety application value of the thermoplastic elastomer poly(styrene-b-isoprene-b-styrene) block copolymer (SIS) with different block ratios were explored to enhance the thermal stability and mechanical strength of the cross-linked polyacrylonitrile (PAN) membranes by vulcanization cross-linking and heat treatment. Among these membranes, the sample named the S/PAN/SIS-4019 separator was confirmed to be a self-closing separator that can cope with the thermal runaway, attributing to the continued fusion of the SIS soft and hard segments in the cross-linked structure under high-temperature heat treatment. Moreover, the tensile strength of S/PAN/SIS-4019 separator increased to 17.49 MPa, which was better than that of Celgard 2400, PAN, and other inlay separators. Using S/PAN/SIS-4019 as a battery separator, lithium-ion batteries showed a superior electrochemical performance compared to the usage of Celgard 2400. Owing to the stable pore structure and thermally protected self-shutdown mechanism, the overall properties of the obtained cross-linked separator were improved in terms of higher thermal stability, high ionic conductivity, and electrochemical properties.