In this work, we study the fission process of large micelles by using dissipative particle dynamics. In general, there exist four different stages during a fission process. For the first stage, the morphological transition to the dumbbell intermediate structures occurs due to a perturbation, in this case, a change in head-head interaction. Then, in the next stage the dumbbell-like intermediate structure fluctuates for a longer or less time until it reaches mechanical instability. Simulation results indicate that the fluctuation of the intermediate structure in this stage can be regarded as a nucleation process. In the third stage, the neck breaks as a result of continuous narrowing. In the last stage the two or more freshly formed, small micelles retract and equilibrate to their final shapes. Simulation results demonstrate that the first, second and third stages are characterized by distinct dynamic features, depending on the surfactant architecture. It is found that surfactant architecture controls the micelle fission process, especially for the second stage, similar to the way it controls the size and shape of the aggregates at equilibrium. Since for most cases it is the second stage that dominates the lifetime of a micelle, we suggest that the molecule packing parameter is not only a predictor of the shape and size of aggregates, but also a predictor of kinetic properties for micelle fission.