At present, the optimal design of linear pyrotechnic separation device mostly depends on experiments, which is not only costly but also low efficient. Herein, a numerical model was developed with arbitrary Lagrangian-Eulerian method for a typical linear pyrotechnic separation device. The numerical model was validated via pyrotechnic separation experiments and photonic Doppler velocimetry, and it was found to have reasonable accuracy. The model was applied to study the mechanical mechanism of the transient separation process of the pyrotechnic separation device. The influence of multiple factors on the critical characteristic parameters was also studied quantitatively, such as effective plastic strain of the key areas of the device. It is found that the linear density of the detonating cord and the bottom radius of the v-notch of the separation plate have significant influence on the separation process. In addition, the material of the protection plate, the angle of the v-notch and the dimension of the rectangular notch of the separation plate also have a certain influence on the separation process, however, the influence is less than that exerted by the linear density of the detonating cord and the bottom radius of the v-notch. The study can provide a foundation for optimal design of the typical linear pyrotechnic separation device.