We present the results of a survey of $N$-body simulations aimed at studying the effects of the long-term dynamical evolution on the stellar mass function (MF) of multiple stellar populations in globular clusters. Our simulations show that if first-(1G) and second-generation (2G) stars have the same initial MF (IMF), the global MFs of the two populations are affected similarly by dynamical evolution and no significant differences between the 1G and the 2G MFs arise during the cluster’s evolution. If the two populations have different IMFs, dynamical effects do not completely erase memory of the initial differences. Should observations find differences between the global 1G and 2G MF, these would reveal the fingerprints of differences in their IMFs. Irrespective of whether the 1G and 2G populations have the same global IMF or not, dynamical effects can produce differences between the local (measured at various distances from the cluster centre) 1G and 2G MFs; these differences are a manifestation of the process of mass segregation in populations with different initial structural properties. In dynamically old and spatially mixed clusters, however, differences between the local 1G and 2G MFs can reveal differences between the 1G and 2G global MFs. In general, for clusters with any dynamical age, large differences between the local 1G and 2G MFs are more likely to be associated with differences in the global MF. Our study also reveals a dependence of the spatial mixing rate on the stellar mass, another dynamical consequence of the multiscale nature of multiple-population clusters.