Understanding the atomistic mechanisms of relaxation dynamics in metallic glasses remains a longstanding challenge. Here, using microsecond time scale molecular dynamics simulations, three main relaxation stages in metallic glasses are identified. At about 0.6T, chemical composition plays a dominant role in the relaxation, manifested by stress accumulation and only minimal variations in structure. As T approaches, the confluence of structural heterogeneity and chemical composition leads to the decoupling of relaxation mechanisms. At this temperature, the relaxation results in a structure with a lower energy state and a lower level of stress. In the supercooled liquid regime, an extensive increase in the number of closed-packed icosahedral clusters is responsible for accelerated structural relaxation while their packing frustration leads to the accumulation of intrinsic residual stresses in the glass. The atomistic origin of these dynamic relaxation modes is discussed in terms of structural, chemical composition and stress variations.