Fully atomistic simulations and a sandwich plate model are used to study the dynamic behavior of twisted 3R-MoS2 bilayers. The simulations demonstrate that for a very small twist angle, the Moiré pattern leads to the symmetry breaking of the interlayer van der Waals energy on the scale of tens of nanometers and causes the dynamic behavior of twisted 3R-MoS2 bilayers to show strong position dependence. In particular, obvious mode pair splitting is observed in twisted 3R-MoS2 bilayer resonators where the interlayer van der Waals energy distribution is nonaxisymmetric. An analysis of the results of these molecular dynamic calculations shows that this behavior can be well explained using the sandwich plate model considering the nonuniform interlayer shear effect. Moreover, the twisted 3R-MoS2 bilayer relaxation mechanism involves the transition from AA stacking order with higher interlayer van der Waals potential energy to AB or BA stacking order, resulting in local buckling in the bilayers. The natural frequencies of resonators dominated by AA domains are much lower than those of resonators dominated by AB domains and even less than those of single-layer 3R-MoS2. Furthermore, as the radius increases, the frequency shows an abnormal trend, and a frequency gap is observed in the resonators dominated by AA domains.