To address the challenges of low positioning accuracy and poor robustness caused by the strong nonlinear coupling of piezoelectric hysteresis, mechanical friction, and transmission backlash in the macro-micro composite-driven cell injection mechanism, an adaptive fast non-singular terminal sliding mode (FNTSM) control strategy is proposed. This strategy aims to eliminate dependence on precise dynamic models and achieve cross-scale precise motion control. First, a dynamic model of the piezoelectric-driven cell injection mechanism is established, considering uncertainties such as hysteresis, friction, and other perturbations. Then, to overcome the dependence on the prior knowledge of disturbance bounds and the chattering issue in traditional sliding mode control, a FNTSM controller is designed that integrates time delay estimation (TDE) technology with adaptive gain adjustment. This controller uses TDE to estimate and compensate for lumped disturbances in real-time, ensuring system states converge within a finite time through FNTSM. Additionally, a PID-type sliding mode surface is introduced, and an adaptive law is designed to dynamically adjust the sliding mode surface parameters, enhancing the system’s ability to suppress strong time-varying disturbances such as friction coefficient changes and load mutations, as well as improving response speed. Experimental results show that in tracking a sine wave trajectory, the controller's root mean square error percentage is 1.39%, with a maximum tracking error percentage of 4.79%. Compared to the traditional PIDSM controller, the maximum tracking error is reduced by 50.9%. In comparison with the recently proposed PIDSMC-RBF advanced controller, the maximum tracking error percentage is reduced by 9.28%. The proposed controller effectively improves the trajectory tracking accuracy of the cell injection mechanism under cross-scale motion, providing a reliable technological solution for micro-manipulation operations.