Hypersonic stage separation is a significant process for the future two-stage-to-orbit (TSTO) vehicle. Strong and complex interstage aerodynamic interference may result in drastic aerodynamic forces and moments, potentially conflicting with the safe separation. Therefore, the dynamic stability of the vehicle during separation is critical to aerospace safety. In this study, numerical analysis of a hypersonic flow with Ma = 6.7 past a parallel-staged TSTO vehicle during stage separation is performed by laminar flow simulations. The TSTO vehicle consists of a wave-rider and a spaceplane as booster and orbiter, respectively. Considering the different centers of gravity for the orbiter during separation, the longitudinal dynamic stability of the orbiter is analyzed based on the dynamic characteristic of the center of pressure (CoP) in different cases. The dynamic separation behavior, aerodynamic characteristics, and typical flowfield patterns are clarified. Moreover, the derivative of CoP to time is proposed and analyzed in detail, which serves as an indicator to determine the dynamic stability and the safe stage separation. A safety separation judgment criterion is also proposed based on the CoP dynamic characteristics for the TSTO vehicle, and the mechanism of CoP variations associated with the unsteady aerodynamic interference during stage separation is revealed.