The competition of intense-field multiple-detachment with efficient photodissociation of F¯ is studied as a function of laser peak intensity. The main product channels are disentangled and characterized by 3D coincidence fragment imaging. The presented kinetic energy release spectra, angular distributions, as well as two-color pump-probe measurements allow identification of competing sequential and nonsequential mechanisms. Dissociative detachment, producing two neutral atoms (F + F), is found to be dominated by a sequential mechanism of photodissociation (F¯ + F), followed by detachment of the atomic anion fragment. In contrast, dissociative ionization (F + F) shows competing contributions of both a sequential two-step mechanism as well as a nonsequential double-detachment of the molecular anion, which are distinguished by the kinetic energy released in the dissociation. Triple-detachment is found to be nonsequential in nature and results in Coulomb explosion (F + F). Furthermore, the measured kinetic energy release for dissociation on the Σ state provides a direct measurement of the F¯ dissociation energy, D = 1.26 ± 0.03 eV.