Capturing the dynamic character of metal nanoparticles under the reaction conditions is one of the major challenges within heterogeneous catalysis. The role of nanoparticle dynamics is particularly important for metal alloys as the surface composition responds sensitively to the gas environment. Here, a first-principles-based kinetic Monte Carlo method is developed to compare the dynamics of dilute PdAu alloy nanoparticles in inert and CO-rich atmospheres, corresponding to reaction conditions for catalyst deactivation and activation. CO influences the dynamics of the activation by facilitating the formation of vacancies and mobile Au-CO complexes, which are needed to obtain CO-stabilized Pd monomers on the surface. The structure of the catalyst and the location of the Pd monomers determine the rate of deactivation. The rate of catalyst deactivation is slow at low temperatures, which suggests that metastable structures determine the catalyst activity at typical operating conditions. The developed method is general and can be applied to a range of metal catalysts and reactions.