The gyroscope established on quantization vortices formed from exciton-polariton Bose-Einstein condensate has important potential applications in the field of quantum guidance. Thus, we assume a concept of quantum gyroscope based on Sagnac effect of the superposition states of quantum vortices existing in exciton-polariton condensates. To study the gyroscopic effect of superimposed vortices, which is the core issue of the project, it is essential to study the dynamic characteristics in the case of system rotating. Therefore, in this paper, the stability and dynamics of positive-negative vortex superposed states of two-dimensional exciton-polariton condensate in the disordered potential are studied under the rotation of the semiconductor microcavity, thereby laying a foundation for studying the gyroscopic effect of the superposed state of exciton-polariton condensates in the semiconductor microcavity. On the basis of reconstructing the mono-component Gross-Pitaevskii equation under the rotational situation, a numerical model with Coriolis items is constructed by the Runge-Kutta method and the finite difference time domain method, which is capable of depicting the rotation of the system. Moreover, the real-time evolution process of positive-negative vortex superposed states with different topological charges and the relationship between the number of steady-state local particles and the angular speed of the rotation of semiconductor microcavity are investigated by the real-time evolution method when the semiconductor microcavity is rotated. In the meantime, the relationship between the rotation speed in the excitation of vortex superposed states and the rotation speed of the semiconductor microcavity is also studied in the presence of the influence of the rotation speed of the semiconductor microcavity on the phase stability of vortex superposed states. According to the study, the rotation speed of the semiconductor microcavity has a significant influence on the evolution process and dynamic characteristics of vortex superposed states of exciton-polariton condensates. The rotation of the exciton-polariton system will accelerate the evolution of superimposed vortices, and overly rapid rotary rate will signalize the fluctuation of the local particle number thus the system unstability occurs. Moreover, along with the system rotation, the exciton-polariton superimposed vortices begin to rotate when the evolution approaches to saturation. It is noticeable that the angular acceleration of superimposed vortices is positively associated with the system rotary rate. Further, the topological charge has a significant influence on the rotation rate of exciation region of superposition state of vortices that it rotates more slowly when the topological charge increases but lower evolution stability simultaneously. These findings possess important guiding significance for establishing the quantum gyroscope in the future.