The drag experienced by the nose of an aircraft varies significantly under different incoming flow conditions. In order to reduce the aerodynamic force on the nose of the (hypersonic) supersonic vehicle, the numerical simulation approach has been used to analyze the drag reduction laws and mechanisms of a blunt-body vehicle with the aerospike-counterflowing jet composite approach under different incoming flow dynamic pressures. The effects of two environments with H = 0.1 km and H = 30 km, as well as the influence of different incoming Mach numbers on the drag reduction at H = 0.1 km were investigated. The research has shown that there exists a minimum overall drag value for the vehicle under different dynamic pressures, while the variation in the wall pressure is related to the actual operating conditions. The recirculation zones at the aerospike and in front of the blunt body are important flow structures that affect the drag reduction. When the jet total pressure ratio increases, the position of the recirculation zone at the head of the drag reduction rod moves away from the central axis of the model. When the incoming flow dynamic pressure is higher, the separation point of the recirculation zone in front of the blunt body is located further downstream, and the reattachment point is related to the incoming flow and jet conditions, aligning with the trend of variation of the position of the maximum pressure on the blunt body wall. As it can effectively push away the shock wave, the enhanced drag reduction effect of the jet is significant when the incoming flow dynamic pressure is higher. However, the high jet pressure resulting from high dynamic pressure needs to be considered in the actual design. Furthermore, the complex turbulent flow field formed by the high dynamic pressure incoming flow and the jet is worthy of further study by means of the large eddy simulation.