Offshore oil and gas has effectively alleviated the global shortage of oil and gas resources, and drilling operations are becoming increasingly frequent. However, the cuttings discharged during surface drilling are transported and deposited to form cuttings piles, which pose a serious threat to the marine ecological environment. In this study, we consider the randomness and uncertainty of cuttings movement to divide the transport process into parabola and collision motion between the moving particles and slope particles after falling on the slope surface of cuttings piles. Through specific analysis of the stress state of a single particle in the transport process and changes in momentum distribution of the particle swarm, the evolution model of the morphological distribution of cuttings piles and the nearby flow field is established. This model can quantitatively analyze the evolution law of the morphological distribution of cuttings piles under the action of ocean current and the disturbance law of the flow field near the cuttings piles caused by the invasion of cuttings particles. Comparing the measured data at an offshore drilling field and prediction results of the model of Sun et al. (2020), the relative error of the model amounts to less than 15%, which demonstrates its rationality. The simulation results show that the morphological distribution of cuttings piles and the nearby flow field change significantly under the action of ocean current, and the intensity of evolution is related to the current velocity and cuttings size, which is of great significance for the quantitative analysis of the evolution of cuttings piles under the action of ocean currents and accurate prediction of their morphological distribution.