A theoretical study of the thermodynamic equilibrium between force-induced tether formation and the adhesion of vesicles mediated by specific ligand-receptor interactions has been performed. The formation of bonds between mobile ligands in the vesicle and immobile receptors on the substrate is examined within a thermodynamic approximation. The shape of a vesicle pulled with a point force is calculated within a continuous approach. The two approaches are merged self-consistently by the use of the effective adhesion potential produced by the collective action of the bonds. As a result, the shapes of the vesicle and the tether, as well as the number of formed bonds in the contact zone, are determined as a function of the force, and approximate analytic expressions for them are provided. The de-adhesion process is characterized by the construction of a phase diagram that is a function of the density of the ligands in the vesicle, the surface coverage by receptors, the ligand-receptor binding affinity, and the reduced volume of the vesicle. In all cases, the phase diagram contains three regions separated by two nonintersecting lines of critical forces. The first is the line of onset forces associated with a second-order shape transition from a spherical cap to a tethered vesicle. The second line is attributed to the detachment forces at which a first-order unbinding transition from a tethered shape to a free vesicle occurs.