The service performance of materials under intense dynamic loading is regarded as a core scientific issue concerning structural safety. An investigation was conducted using a modified split Hopkinson pressure bar experimental platform combined with the digital image correlation (DIC) method and Lagrangian analysis, through which the dynamic constitutive characteristics and spallation behavior of four materials—grey sandstone, yellow sandstone, granite, and polymethyl methacrylate (PMMA)—were studied under an impact velocity of 20 m/s. The experimental results show that granite exhibits the highest peak stress of 68.5 MPa but shows significant brittle characteristics with the highest number of cracks. The peak stresses of grey sandstone and yellow sandstone are measured as 43.5 MPa and 39.4 MPa, respectively, both displaying typical brittle fracture features. Under the same impact velocity, PMMA is observed to experiences only minor spallation, with the lowest peak stress of 26.4 MPa, and its stress-strain curve is found reveals notable ductility. Using the free-surface velocity pull-back technique, the spall strengths of the materials are calculated based on the wave velocity at the spall location, combined with the maximum velocity and the reflected velocity difference. The results show that the spall strength of grey sandstone is 16.2 MPa, while that of granite is 31.1 MPa. The Lagrangian is effectively used effectively to reveals the dynamic constitutive response of the materials, providing an important theoretical basis for the anti-impact design of multi-material structures. Furthermore, the research results are considered to lay a foundation for a deeper understanding of the spallation failure mechanisms of different materials under dynamic loading.