The separation of micro and nanoscale colloids is a necessary step in most biological microassay techniques, and is a common practice in microchemical processing. Chemical waves are frequently encountered in biochemical systems driven far from equilibrium. Here, we put forward a strategy for separating small suspending colloids by means of their surfing on substrate chemical wavefronts. The colloids with catalytic activities sensitive to the substrates are activated to show self-propulsion and consequently exhibit a chemotactic response to the traveling wavefronts, which results in their spontaneous separation from the multicomponent complex mixture via self-diffusiophoresis. The dynamics of the process is analyzed through a particle-based simulation. In addition, it is found that separation can be carried out according to particle size. The mechanisms underpinning the chemical and physical separation processes are discussed, and the dependencies on the reaction rate constant and particle size are presented. The results may prove relevant for further experimental and theoretical studies of separation in complex active environments.