Earthquake loss estimation in composite-steel moment resisting frames (MRFs) necessitates a proper estimation of the level of damage in steel beam-to-slab connections. These usually feature welded headed shear studs to ensure the composite action between the concrete slab and the steel beam. In partially composite steel beams, earthquake-induced damage in the shear studs and the surrounding concrete occurs due to shear stud slip demands. Within such a context, this paper proposes shear slip-based fragility functions to estimate the probability of being or exceeding four damage states in steel beam-slab connections. These damage states include cracking and crushing of the concrete slab in the vicinity of the shear studs, as well as damage in the shear studs themselves. The developed fragility functions are obtained from a gathered dataset of 42 cyclic push-out tests. They incorporate uncertainty associated with specimen-to-specimen variability, along with epistemic uncertainty arising from the finite number of available experimental results. An application of the proposed fragility functions is conducted on a six-story building with composite-steel MRFs. It is shown that steel beam-slab connections along the building height only exhibit light cracking (i.e., crack sizes of 0.3 mm or less) at design basis seismic events. At seismic intensities associated with a low probability of occurrence seismic event (i.e., return period of 2475 years) the nonlinear building simulations suggest that the 25% reduction of the shear stud resistance in steel beam-slab connections with beam depths of 500 mm or less is not imperative to maintain the integrity of the shear stud connectors.