The unsuitably designed powertrain mount may cause jittering and shrugging during the starting and shifting processes of the vehicle, which seriously affects the comfort of using the vehicle. However, the influence of mounts on vehicles has been neglected in previous studies. In view of the above problems, this study establishes a DCT vehicle coupling dynamic model, considering six degrees of freedom of the powertrain mount and the engine dynamic torque, nonlinear characteristics of a dual-mass flywheel, time-varying stiffness of gear systems, and other factors. Furthermore, the effect of mounts on the longitudinal dynamic characteristics of the vehicle is studied during the starting, shifting, and tip-in/tip-out process. The results show that under typical working conditions, the mount and its stiffness and damping affect the fluctuation frequency and amplitude of the jerk. When the torque of the vehicle transmission system changes greatly, such as under starting and tip-in/tip-out conditions, the mount has a great impact on the dynamic performance of the vehicle. Simultaneously, the engine torque fluctuation can act on the vehicle through the mount, which has an impact on the jerk of the vehicle. A comparison with vehicle test results reveals that the DCT coupling dynamic model can reflect the law of the effect of the mount on the vehicle performance and verify the rationality of the model. Under typical working conditions, when the influence of the mount is not considered in the vehicle dynamic’s modeling, there is a large error of the jerk between the simulation results and the actual situation. The results provide a reference for optimizing the parameters of the mount and improving the dynamic characteristics of DCT vehicles.