This study aims to understand the progressive collapse mechanism of concrete-filled steel tubular (CFST) frame-core wall hybrid structures when local components are destroyed. Under the failure condition of columns and core walls on the 1st, 17th, and 33rd floors, nonlinear dynamic analysis of a 33-story CFST frame-core wall hybrid structure is carried out based on ABAQUS fiber beam and multi-layer shell elements by using the material constitutive subroutine iFiberLUT. The anti-progressive collapse mechanism of the remaining structure is also studied. When the components are destroyed, the lowest displacement response of the upper node occurs on the 1st floor, a larger displacement response occurs on the 17th floor, and the largest one occurs on the 33rd floor. Compared with that in the failure condition of the shear wall, the vertical displacement of the upper joints is greater and vibrations are more obvious when a column is destroyed. The influence of different working conditions on the core wall is weak, and the core wall enhances the film effect of the floor slab; it also improves the anti-progressive collapse capacity of the structure. Moreover, the path of inertial forces follows the "shortest path principle" when typical components are destroyed. The slab and core wall effectively improve the redundancy load path and integrity of the hybrid structures.