Molecular dynamics simulations are performed to investigate the dynamic properties and microstructure of Cu(100-x)Agx (x = 0, 25, 45.8, 75, 100) melts. A dynamic crossover reflecting the Arrhenius-to-non-Arrhenius transition and the breakdown of the Stokes-Einstein relationship is found in the melts except for pure Cu and Ag. Different from Cu75Ag25 and Cu25Ag75 melts of which the crossover temperature Tc is below the liquidus temperature, the Tc of Cu54.2Ag45.8 eutectic melt is about 115 K above the eutectic temperature. Around the crossover temperature, abrupt enhancement in the dynamic heterogeneity and breaking of the Stokes-Einstein relationship are also observed. Structural analyses based on chemical short-range order and local topological atomic stacking reveal that the rapid increase of the number of slow particles, the abruptly expanding difference in local atomic structure and the resultant change in diffusion mechanism trigger the abnormal dynamic behavior. The same species of atoms tend to gather into clusters especially at lower temperature. In contrast to Ag atoms whose migration capability does not vary with their positions in the Ag clusters, Cu atoms move slower due to the higher degree of order when they are in the center of the Cu clusters. A roughly empirical relationship between the dimensionless dynamic property D* and excessive entropy S2 is revealed by using the extended scaling law to the Cu-Ag melts. These findings are highly helpful for an in-depth understanding of the dynamics of eutectic melts.