The switching capabilities and RF performance of graphene nanoribbon field-effect transistors (GNRFETs) in the presence of electron-phonon scattering are examined. Self-consistent atomistic simulations based on the nonequilibrium Green's function (NEGF) formalisms are used. We have studied the influence of incoherent transport on the most important digital parameters such as Ion, Ioff, Ion/Ioff, the subthreshold swing, and the drain-induced barrier lowering (DIBL) versus the channel length. Furthermore, the effects of phonon scattering on the gate capacitance and the transconductance are investigated in order to calculate the intrinsic cut-off frequency, switching delay, and the power-delay product of non-ballistic GNRFETs. We have shown that band-to-band tunneling regime is dominated by the phonon-assisted tunneling. Therefore, the off-current and the sub-threshold swing are deteriorated by this phenomenon. Furthermore, the scattering results in a decrease of intrinsic cut-off frequency and increase of the gate delay and energy consumed per switching event.