This paper presents a passivity-based twisting sliding mode control (PBSMC) approach for series elastic actuators (SEAs). To address the time-varying position trajectory tracking control problem in SEAs, a fourth-order dynamic model is developed to accurately characterize the system. The control framework comprises an internal loop and an external loop controller, each designed to ensure precise trajectory tracking. The internal loop controller manages the second derivative of the joint trajectory position error, while the external loop focuses on the error itself. Both controllers are based on the PBSMC methodology to reduce complex nonlinear disturbances and minimize tracking errors. The finite-time convergence of the proposed method is rigorously analyzed. The performance and advantages of the method are evaluated and compared through various simulations.