The F 1s core level photoionization of the ionic molecular radical HF+ has been studied using the photon-ion merged-beams technique at a synchrotron radiation source. Upon analyzing kinetic energy release (KER) dependent photoion yield spectra, complex ultrafast dissociation dynamics of the F 1s core hole excited σ∗ state can be revealed. By means of configuration-interaction electronic structure calculations of the excited molecular potential energy curves, this complex process can be attributed to a spin-dependent dissociation of the excited σ∗ biradical state.