To examine the influence of impact angles on the damage characteristics of semi-combustible cartridge charges, a dynamic finite element model for drop impact is established based on nonlinear finite element theory. The drop impact behavior of the semi-combustible cartridge charge is simulated through ANSYS/LS-DYNA software. Numerical simulations are performed to evaluate the impact responses of the charge at four typical angles—30°, 45°, 60°, and 90°—when dropped from a height of 1.2 m onto a concrete surface. This study investigates the stress response, deformation characteristics, and overload variations under various impact conditions, along with the deformation and damage patterns of the combustible cartridge, metal base, and projectile. The results demonstrate that the risk of damage to the combustible cartridge markedly increases as the impact angle decreases, with the most severe damage occurring at a 30° impact. When the impact angle is below 45°, localized failure of the combustible cartridge occurs. At impact angles of 30°, 45°, and 60°, the safety-critical risk region is concentrated in the stepped transition zone of the adhesive interface between the combustible cartridge and the metal base. Conversely, at a 90° impact, the safety-critical risk region shifts to the stepped transition zone of the adhesive interface between the combustible cartridge and the projectile. Furthermore, as the impact angle increases, the maximum overload experienced by the charge rises, while the time to peak overload decreases. These findings establish a theoretical foundation for optimizing the impact-resistant structural design and safety assessment of semi-combustible cartridge charges.