As the only component of the Carrier-Based Aircraft in contact with the deck, the tire’s dynamic characteristics are directly related to the stability and safety of the catapult-assisted takeoff. During the catapult-assisted takeoff process, the tire inevitably undergoes damage due to factors such as variable loading and high acceleration. One significant damage mechanism of the rubber material is Mullins damage, which leads to a considerable reduction in the rubber modulus and consequently has a substantial impact on the dynamic characteristics of the tire, threatening the safety of Carrier-Based Aircraft during takeoff and landing. To address this issue, this paper considers the severe radial load and the high angular acceleration during catapult-assisted takeoff, and the finite element analysis software ABAQUS is used to simulate the movement and deformation of the main landing gear tire during the catapult-assisted takeoff of the Carrier-Based Aircraft. The distribution of Mullins damage caused by a single takeoff and its effects on tire stiffness, tire–ground contact, and vibration characteristics are investigated. The results show that the asynchronous behavior between the tire’s rotation angle and radial deformation during catapult-assisted takeoff leads to excessive local deformation of the tire, resulting in a significantly non-uniform circumferential distribution of damage after takeoff, which causes circumferential non-uniformity in tire stiffness. Radial deformation increases significantly due to Mullins damage, and the tangential contact force is proportional to the radial contact force. A comparison of the tire’s vibration modes before and after damage shows a decrease in natural frequencies across all modes, and the modal shapes, especially the circumferential modes, are significantly affected by the circumferential non-uniformity in tire stiffness and damage distribution. This paper provides a theoretical basis for understanding the distribution of Mullins damage and its impact on the dynamic characteristics of the tire during catapult-assisted takeoff, thereby improving tire performance and ensuring takeoff safety.