While ensuring thermal safety is critically required in the operation of the composite energetic material, the cutting temperature is a crucial parameter that must be investigated and controlled in its cutting process to avoid thermal explosion. In this paper, we elucidate the mechanisms of heat generation and conduction during the cutting process of a composite energetic material by establishing a microstructure-based finite element (FE) simulation model considering thermal effects. Specifically, we simulated the cutting process of the composite energetic material by FE simulations, with a focus on the variations in the cutting force, the initiation and conduction of the cutting temperature, and the correlation of the damage behavior of the composite energetic material. Subsequently, we conducted a parametric investigation of the effect of cutting speed on the damage behavior and cutting response of the composite energetic material. This paper provides valuable insights for the exploration of the cutting processes of composite energetic materials.