Supercritical carbon dioxide (SC-CO2) fracturing technology, as a promising waterless fracturing technology, plays an increasing role in the development of tight reservoirs. Based on computational fluid dynamics software, the flow state of CO2 in the reservoir was analyzed, the characteristics of CO2 were characterized, a numerical simulation method of SC-CO2 fracturing based on cohesive units was proposed, and a fluid–solid coupling numerical model of SC-CO2 multistage and multicluster fracturing was established. The dynamic interaction between fractures in the process of segmented and multicluster fracturing was studied, and the final shape of multicrack propagation was discussed. The results indicated that the interaction between cracks generated by single-stage and three-cluster fracturing will keep the two main cracks away from each other, which is helpful to increase the control area of the cracks. The perforation phase angle is an important parameter to control crack morphology, and an improper perforation phase angle setting may turn new cracks into existing cracks. During two-stage and four-cluster fracturing, the directions of adjacent perforation cracks in each stage are distributed at intervals; the geometric distribution of cracks in the left and right clusters is relatively uniform, and the crack lengths generated by the two inner perforation positions in each stage are significantly greater than the crack lengths outside. The three-stage and single-cluster fracturing is conducive to the formation of a crack network, the crack length is basically linearly distributed with time, and the maximum crack width increases slightly in sequence for the three stages. The more the fractured perforations per cluster for the same wellhead injection rate, the lower the crack width. This study is expected to provide theoretical guidance for SC-CO2 multistage and multicluster fracturing in tight reservoirs.