The typical framework of replicator dynamics in evolutionary game theory assumes that all mutations are equally likely, meaning that the mutation of an evolving inhabitant only contributes constantly. However, in natural systems in biological and social sciences, mutations can arise due to their repetitive regeneration. The phenomenon of changing strategies (updating), typically prolonged sequences repeated many times, is defined as a volatile mutation that has been overlooked in evolutionary game theory. Implementing a repeated time framework introduces a dynamic mutation aspect incorporated with the pairwise Fermi rule. Network structure, ubiquitous in many natural and artificial systems, has significantly affected the dynamics and outcomes of evolutionary games. We examine the evolution of the pairwise game in terms of dilemma strength. It is revealed that mutation intensity can influence evolutionary dynamics. We also demonstrated that the obtained outcomes run by the deterministic and multi-agent simulation (MAS) process present similar stability regions for both linear and non-linear dynamics, even in various game classes. In particular, the most stimulating effect is detected for the relationship between the fraction of cooperation and the fraction of the mutated individuals, as inclination tends to provide an increasing tendency and supporting defection in the opposite case. In conclusion, we identified a form of volatile mutation as a form of noise that, under certain situations, could be used to enhance cooperation in social systems and design strategies for promoting cooperation in networked environments.