This study underscores the profound influence of rock joints, both persistent and non-persistent with rock bridges, on the stability and behavior of rock masses—a critical consideration for sustainable engineering and natural structures, especially in rock slope stability. Leveraging the lattice spring-based synthetic rock mass (LS-SRM) modeling approach, this research aims to understand the impact of persistent and non-persistent joint parameters on rock slope stability. The Slope Model, a Synthetic Rock Mass (SRM) approach-based code, is used to investigate the joint parameters such as dip angle, spacing, rock bridge length, and trace overlapping. The results show that the mobilizing zones in slopes with non-persistent joints were smaller and shallower compared to slopes with fully persistent joints. The joint dip angle was found to heavily influence the failure mode in rock slopes with non-coplanar rock bridges. Shallow joint dip angles led to tensile failures, whereas steeper joint dip angles resulted in shear-tensile failures. Slopes with wider joint spacings exhibited deeper failure zones and a higher factor of safety, while longer rock bridge lengths enhanced slope stability and led to lower failure zones. The overlapping of joint traces has no apparent impact on slope stability and failure mechanism. This comprehensive analysis contributes valuable insights into sustainable rock engineering practices and the design of resilient structures in natural environments.