More than 100 structurally diverse point mutations leading to aggregation in the dimeric enzyme Cu, Zn superoxide dismutase (SOD1) are implicated in familial amyotrophic lateral sclerosis (FALS). Although SOD1 dimer dissociation is a known requirement for its aggregation, the common structural basis for diverse FALS mutations resulting in aggregation is not fully understood. In molecular dynamics simulations of wild-type SOD1 and three structurally diverse FALS mutants (A4V, G37R, and H46R), we find that a common effect of mutations on SOD1 dimer is the mutation-induced disruption of dynamic coupling between monomers. In the wild-type dimer, the principal coupled motion corresponds to a "breathing motion" of the monomers around an axis parallel to the dimer interface, and an opening-closing motion of the distal metal-binding loops. These coupled motions are disrupted in all three mutants independent of the mutation location. Loss of coupled motions in mutant dimers occurs with increased disruption of a key stabilizing structural element (the beta-plug) leading to the de-protection of edge strands. To rationalize disruption of coupling, which is independent of the effect of the mutation on global SOD1 stability, we analyze the residue-residue interaction network formed in SOD1. We find that the dimer interface and metal-binding loops, both involved in coupled motions, are regions of high connectivity in the network. Our results suggest that independent of the effect on protein stability, altered protein dynamics, due to long-range communication within its structure, may underlie the aggregation of mutant SOD1 in FALS.