The heterogeneity of the reservoir plays a crucial role in influencing the propagation of multi-cluster hydraulic fractures in horizontal wells. To explore this impact, a seepage-stress-damage coupled model was developed in this study for analyzing the competitive propagation of multi-cluster fractures utilizing the finite-discrete element method. Utilizing the model, a random assignment program has been developed to establish the coupling distribution of mechanical parameters between matrix elements and discrete elements for characterizing the reservoir heterogeneity. Simultaneously, a wellbore flow model describing the pressure drop of fracturing fluid flow is developed by introducing pipe flow element and fluid connection element, enabling the realization of dynamic flow distribution. Based on the developed model, an investigation is conducted into the impact of pumping rates, fracturing fluid viscosity, and perforation parameters on the fracture propagation of multi-cluster fracturing. The study findings suggest that as reservoir heterogeneity increases, the distribution of rock strength becomes more uneven, resulting in a more complex morphology of fracture propagation. Higher pumping rates lead to elevated pressure within fractures, thereby facilitating the uniform propagation of multi-cluster fractures, particularly in reservoir characterized by medium to high heterogeneity. Increasing the viscosity of fracturing fluid can diminish the tortuosity of multi-cluster fracture propagation, albeit with a somewhat limited enhancement in uniformity. As reservoir heterogeneity intensifies, the interference between fractures escalates, necessitating a reduced number of perforations to heighten perforation friction and enhance the balanced propagation of multi-cluster fractures. This research offers theoretical guidance and a scientific foundation for the design of schemes and optimization of parameters in staged multi-cluster fracturing technology for horizontal wells in heterogeneous reservoirs.