Due to the important strategic position of Pumped Storage Power Plants (PSPP) in global energy upgrading, conducting in-depth research on the various operating conditions of pump turbine units is important for their safe and stable operation. This study sought to clarify the gas–liquid phase motion and the nonlinear chaotic characteristics of the process of exhaust and pressurization in pump mode; with the simplified objective model proposed here, a visualization of the process is achieved using data-driven methods, and the nonlinear characteristics of gas–liquid phase motion during the process are theoretically demonstrated. A method that combines data-driven and chaotic analysis is proposed to qualitatively and quantitatively analyze the force and torque time-series signals of the runner under different exhaust rates. The results indicate that the chaotic characteristics of the force signals and torque signals of the runner are not in a single linear relationship with the exhaust rates. Therefore, this research also provides guidance on exhaust rates with the aim of informing actual engineering practice, the purpose of which is to reduce the vibration amplitude caused by repetitive torque and improve the stability of the unit operations.