With the development of mud shield tunnel construction technology, the demands on the working performance of a mud pump are becoming higher and higher. As one of the critical components of a mud pump that is easy to wear, the performance of the piston directly affects the operational efficiency and lifespan of the mud pump. The bionic shape of the piston was designed under the guidance of non-smooth surface characteristics of natural organisms to enhance friction and wear performance as well as longevity. The stress field and temperature field characteristics of the pistons with three bionic structures (pit, stripe, and prismatic) were analyzed based on finite element simulation. The stress field analysis results indicated that, for the prismatic shape and pit shape pistons, the maximum stress was concentrated in the lip regions, and both of them bore large stress at the root. For the stripe-shaped piston, the stress was dispersed on both sides of the stripe structure, the stress at the root was small, and the stress gradient along the axial direction was relatively gentle. The stripe-shaped bionic structure can significantly improve the stress distribution state on the piston surface, and the optimal stripe width was recommended to be between 1 and 1.5 mm. The temperature field analysis results indicated that, for the stripe-shaped piston, the surface temperature and heat flux were the smallest, and the temperature gradient was relatively smaller than that of pit-shaped and prismatic-shaped pistons, so it was easier to dissipate heat. When the stripe width was 1.5 mm, the temperature distribution was the most uniform, and the heat flux in localized areas was the smallest, so the heat generated by friction was relatively easy to discharge in the unit area.