In complex orchard environments, orchard mowing robots are prone to longitudinal slippage because of the characteristics of tires and the adhesion conditions of the road surface, which makes it difficult for the robots to maintain high-precision path tracking and autonomous navigation positioning. This not only affects the accuracy of path tracking but also leads to unstable motion for the mowing robots. To solve the above problems, we take an orchard mowing robot as the control object and establish a cascaded path-tracking controller and an adaptive time domain model based on a kinematics model. By designing a linear error model, an objective function, and constraint conditions for the mowing robot, the optimal linear velocity and angular velocity of the mower are obtained and converted into the speed of the driving wheel. Then, an anti-slip driving controller is designed based on fuzzy control of the slip rate. The slip-rate-based fuzzy controller is constructed according to the real-time speed of the mower and the reference speed of the driving wheel solved by the model predictive controller, and anti-slip driving control is implemented through a combination of a PID controller and a tire dynamics model. To verify the effectiveness of the proposed method, simulation and field experiments are conducted. The experimental results show that the slip rate of the driving wheel of the mower remains within the target slip rate range in the orchard working environment, avoiding excessive driving wheel sliding. Furthermore, the average lateral error of the path-tracking controller is controlled within 0.05 m, and the average value of the longitudinal error is kept within 0.04 m, which satisfies the control accuracy requirements of lawn mower operations. The proposed method provides a reference optimization scheme for improving the path-tracking and motion stability of a mowing robot.