Cutting is a crucial step in the industrial production process, particularly in the manufacture of large structures. In certain spatial positions, using a mobile robot, especially a wall-climbing robot (WCR) with adsorption function, is essential for carrying cutting torches to cut large steel components. The cutting quality directly impacts the overall manufacturing quality. Therefore, effectively tracking the cutting trajectory of wall-climbing cutting robots is very important. This study proposes a controller based on a kinematic model and PID optimization. The controller is designed to manage the robot’s kinematic trajectory, including the torch slider, through the kinematic modeling of the wall-climbing cutting robot (WCCR). The stability of the control law is proven using the Lyapunov function, which controls the linear and angular velocities of the WCCR and the motion speed of the cross slider. Simulations verify that the control law performs well in tracking both straight-line and circular trajectories. The impact of different control law parameters on straight-line trajectory tracking is also compared. By introducing PID optimization control, the controller’s anti-interference capabilities are enhanced, addressing the issue of motion velocity fluctuation when the WCCR tracks curved trajectories. The simulation and experiment results demonstrate the effectiveness of the proposed controller.