In this paper, we use N-body simulations to study the effects of primordial mass segregation on the early and long-term evolution of star clusters. Our simulations show that in segregated clusters early mass loss due to stellar evolution triggers a stronger expansion than for unsegregated clusters. Tidally limited, strongly segregated clusters may dissolve rapidly as a consequence of this early expansion, while segregated clusters initially underfilling their Roche lobe can survive the early expansion and have a lifetime similar to that of unsegregated clusters. Long-lived initially segregated clusters tend to have looser structure and reach core collapse later in their evolution than initially unsegregated clusters. We have also compared the effects of dynamical evolution on the global stellar mass function (MF) of low-mass main-sequence stars. In all cases, the MF flattens as the cluster loses stars. The amount of MF flattening induced by a given amount of mass loss in a rapidly dissolving initially segregated cluster is less than for an unsegregated cluster. The evolution of the MF of a long-lived segregated cluster, on the other hand, is very similar to that of an initially unsegregated cluster.