The use of an approximate reference state wave function mid R:Phi(r) in electronic many-body methods can break the spin symmetry of Born-Oppenheimer spin-independent Hamiltonians. This can result in significant errors, especially when bonds are stretched or broken. A simple spin-projection method is introduced for auxiliary-field quantum Monte Carlo (AFQMC) calculations, which yields spin-contamination-free results, even with a spin-contaminated mid R:Phi(r). The method is applied to the difficult F(2) molecule, which is unbound within unrestricted Hartree-Fock (UHF). With a UHF mid R:Phi(r), spin contamination causes large systematic errors and long equilibration times in AFQMC in the intermediate, bond-breaking region. The spin-projection method eliminates these problems and delivers an accurate potential energy curve from equilibrium to the dissociation limit using the UHF mid R:Phi(r). Realistic potential energy curves are obtained with a cc-pVQZ basis. The calculated spectroscopic constants are in excellent agreement with experiment.