We present a second-order scalar auxiliary variable (SAV) Fourier spectral method for solving the nonlinear fractional generalized wave equation. We first establish the unconditional energy conservation or dissipation of the fully discrete scheme. Then, by employing a temporal-spatial error splitting approach, we derive unconditional optimal error estimates. This analysis overcomes the usual time-step restrictions associated with strongly nonlinear systems, and does not require the global Lipschitz condition on the nonlinear term—an assumption needed in previous works on fractional wave equations. Finally, we present numerical examples to support the theoretical findings.