In this paper, a typical vortex system based on quasi-linear thermal-dynamic equations to reflect the development and extinction of the China Southwest Vortex is established using the vortex motion stability method combined with the outer environmental field and cumulus convective latent heat release. The development and extinction of the China Southwest Vortex in catastrophic weather systems are studied from the aspects of stability and development mechanisms for the primary-stage China Southwest Vortex, the transition mechanism from the primary-stage China Southwest Vortex to the mature vortex, and stability and development mechanisms of the mature China Southwest Vortex. The results show the following: (1) the convergence and divergence of the surrounding flow field is the main factor influencing the development and extinction of the primary-stage China Southwest Vortex, while gravity wave disturbance is the main driving force for the maintenance and development of the primary vortex. Based on the convergence of the external flow field, the gravity wave disturbance must exceed the critical frequency, or the vortex will tend to die out. (2) The convergence and divergence of the surrounding flow field is also the main factor for the transition from the primary vortex to the mature vortex. Based on the convergence of the surrounding flow field, the primary vortex transforms into a mature vortex only when the gravity wave disturbance strongly exceeds the critical frequency and causes the vertical disturbance to become unstable. (3) The convergence and divergence of the external flow field is also the main factor for the development and extinction of the mature China Southwest Vortex. In the early stage, the vortex can be maintained and developed as long as the surrounding flow field converges. In the case of the divergence of the external flow field, the vortex may be maintained for a short time, but eventually dissipates when the gravity wave disturbance exceeds the critical frequency. In the later stage, under the convergence of the surrounding flow field, the vortex can be maintained when the gravity wave disturbance exceeds the critical frequency. However, with the divergence of the surrounding flow field, the vortex may be maintained for a short time, but it will eventually dissipate when the gravity wave disturbance is extremely strong. In addition, the observations of the evolution of China Southwest Vortexes and gravity wave activities under the influence of southwest airflow and atmospheric disturbance in the Western Sichuan Plateau–Sichuan Basin are explained by the above physical mechanism. It is also pointed out that the heating effect can be an obstacle to the development of the China Southwest Vortex by increasing the critical frequency of gravity waves during unstable layer formation, and the divergent environment flow field under the condition of stable layer formation. Therefore, this paper deepens the understanding of the evolution process and anomalous mechanisms of the China Southwest Vortex.