We investigate the effect of a periodic electric field drive on the generalized Aubry-Andr´e model, also known as the Ganeshan-Pixley-Das Sarma (GPD) model, which is well known as a host of mo- bility edges. Our study of the Floquet spectrum of the driven GPD model uncovers the emergence of two distinct Floquet mobility edges, a delocalized–localized (DL) edge in the bounded regime, and a multifractal–localized (ML) edge in the unbounded regime. By mapping the high-frequency effective Hamiltonian to the static GPD model via a Bessel-renormalized hopping, the driven mobil- ity edge formulae follow directly, with drive-induced localization arising naturally at specific values of the driving parameters, where the effective tunneling is coherently suppressed. Combined with numerical diagnostics such as the fractal dimension and inverse participation ratio, we demonstrate that these mobility edges can be effectively controlled by the amplitude and frequency of the electric field drive. Furthermore, the dynamical study of the periodically driven GPD model demonstrates superdiffusive to almost ballistic transport in the bounded regime corresponding to the DL edges, whereas subdiffusive transport is observed in the unbounded regime associated with the ML edges. We also analyze deviations from the high-frequency effective description by explicitly examining the low-frequency driving regime, where significant and counterintuitive deviations in both spectral properties and transport behavior are observed. Our study highlights the interplay of a quasiperi- odic potential and a periodically varying electric field drive as a powerful mechanism to engineer mobility edges and control transport in systems with rich spectral features.