We perform nonequilibrium dynamics simulations of a binary Lennard-Jones mixture in which an external force is applied on a single tagged particle. For the diffusive properties of this particle parallel to the force, superdiffusive behavior at intermediate times as well as giant long-time diffusivity is observed. A quantitative description of this nontrivial behavior is given by a continuous time random walk analysis of the system in configuration space. We further demonstrate that the same physical properties which are responsible for the superdiffusivity in nonequilibrium systems also determine the non-Gaussian parameter in equilibrium systems.