The R&D Building of Zhanjiang Bay Laboratory is a high-rise structure with multiple irregular items exceeding the specification limit, employing a steel frame-shear wall structural system. The outer frame consists of square steel tube concrete columns and solid-web steel beams, while the core shear wall uses a double steel plate concrete composite shear wall. This paper employs the architectural structural calculation software YJK-EP to perform a dynamic elastic-plastic time-history analysis under rare earthquake action. The shear and bending resistance of the shear wall at the maximum shear force and bending moment are checked to meet the requirements of the “Technical Specifications for Concrete Structures of High-rise Buildings”. The maximum inter-story displacement angle meets the requirements of the “Code for Seismic Design of Buildings”. The double steel plate concrete composite shear wall Wall-1, connected to a large-span and heavy-load transfer truss, was verified under significant seismic action using the ABAQUS software. The results indicate that Wall-1 can meet the design target requirements under major earthquake conditions. Finally, a dynamic nonlinear analysis method was employed using MIDAS-GEN software to study the structure’s anti-progressive collapse performance. The results show that under seven different scenarios, the maximum rotational angle of the remaining structural horizontal members is 2.02°, far less than the limit set by GSA, indicating that a progressive collapse did not occur. In the scenario where the corner column is removed, both the maximum shear and bending moment values for Wall-1 are far below its shear and bending resistance capacities, satisfying the load-bearing requirements. The removal of the corner column has a significant impact on the displacement of the columns on the same level nearby, with the peak displacement change rate reaching 702.65%.