Multi-axle Swerve-drive Autonomous Mobile Robots (MS-AGVs) equipped with independently steerable wheels are commonly used for high-payload transportation. In this work, we present a novel model predictive control (MPC) method for MS-AGV trajectory tracking that takes tire wear minimization consideration in the objective function. To speed up the problem-solving process, we propose a hierarchical controller design and simplify the dynamic model by integrating the \textit{magic formula tire model} and \textit{simplified tire wear model}. In the experiment, the proposed method can be solved by simulated annealing in real-time on a normal personal computer and by incorporating tire wear into the objective function, tire wear is reduced by 19.19\% while maintaining the tracking accuracy in curve-tracking experiments. In the more challenging scene: the desired trajectory is offset by 60 degrees from the vehicle's heading, the reduction in tire wear increased to 65.20\% compared to the kinematic model without considering the tire wear optimization.