Finding the lowest-energy structure of a cluster of atoms is an NP-Hard problem with applications in materials science. Genetic Algorithms (GAs) have shown promise in solving this problem due to their ability to explore complex energy landscapes. A critical component of GAs are the mutations, which maintain diversity and helps avoid premature convergence. Despite the existence of various mutation operations for atomic clusters, there is a lack of benchmarking to compare their effectiveness. In this paper, we evaluate the performance of eight mutation operations within a GA framework for optimizing Lennard-Jones clusters. We assess each mutation based on its ability to reach the global minimum (accuracy) and the time required to do so (runtime). Experiments are conducted across population sizes of 8, 15, and 20, with multiple mutation probabilities tested. Results show that the Etching mutation consistently provides the highest accuracy, but at a considerable runtime cost. In contrast, Twist and Random Displacement offer fast convergence with moderate success rates.