Using a sample of simulated galaxy clusters, whose dynamical history can be well known and described, we assess the impact of the ICM internal dynamics on both the thermal and kinetic SZ effects (tSZ and kSZ, respectively). We conclude that the SZ effect can be used as a tool to estimate the dynamical state of galaxy clusters, especially to segregate those clusters with a quiescent evolution from those with a rich record of recent merger events. Our results suggest that the forthcoming observational data measuring the SZ signal in clusters could be used as a complementary strategy for classifying the evolutionary history of galaxy clusters.