Recent experiments provide evidence for photocurrent generation in Dirac systems such as topological-insulator surface states and graphene. Within the simplest picture, the magnitude of the photocurrents is governed by the competition between photoexcitation of particle-hole pairs and current relaxation by scattering. Here, we study the relaxation of photocurrents by electron-electron (e−e) collisions, which should dominate in clean systems. We compute the current relaxation rate as a function of the initial energies of the photoexcited carriers and the Fermi energy. For a positive Fermi energy, we find that collisions of a single excited electron with the Fermi sea can substantially increase the current, while for a single excited hole the current initially decreases. Together these processes partially cancel leading to a relative suppression of the relaxation of the total photocurrent carried by an electron-hole pair. We also analyze the limit of many scattering events and find that while e−e collisions initially reduce the current associated with a single hole, the current eventually reverses sign and becomes as large in magnitude as in the electron case. Thus, for photoexcited electron-hole pairs, the current ultimately relaxes to zero. We discuss schemes which may allow one to probe the nontrivial current amplification physics for individual carriers in experiment.