Galaxy clusters interact with each other through a variety of hydrodynamical and gravitational mechanisms that can both increase and decrease the amount of star formation (SF) present in their member galaxies. Substructure and asymmetry in the distribution and dynamics of cluster galaxies are indicative of past interaction. In this thesis, I study large samples of galaxy clusters to determine if the merging and interaction of clusters preferentially enhances or quenches cluster SF. First, in a sample of 107 nearby clusters in which I measure SF using optical emission lines and substructure using the positions and velocities of member galaxies, I find that clusters with more substructure tend to exhibit more SF, and I reproduce the well-known direct correlation between SF and clustercentric distance and the inverse correlation between SF and density. Second, in a sample of 379 nearby clusters in which I measure SF using WISE photometry and relaxation using the optical surface brightness maps of member galaxies, I find that less relaxed clusters exhibit more SF. These two studies, using different cluster samples and different methods of measuring SF and substructure, arrive at similar conclusions. Finally, I return to the first sample of 107 clusters and introduce the effects of supercluster environment density and morphology into my analysis. I find that clusters in higher-density regions of superclusters exhibit less SF than those at lower densities, a trend preferentially found in filament superclusters. Furthermore, at high densities, clusters in spider superclusters exhibit more SF than those in filament superclusters.