We demonstrate that the nontrivial magnetic texture of antiferromagnetic Skyrmions (AFM Sks) promotes a nonvanishing topological spin Hall effect (TSHE) on the flowing electrons. This effect results in a substantial enhancement of the nonadiabatic torque and, hence, improves the Skyrmion mobility. This nonadiabatic torque increases when decreasing the Skyrmion size, and, therefore, scaling down results in a much higher torque efficiency. In clean AFM Sks, we find a significant boost of the TSHE close to the van Hove singularity. Interestingly, this effect is enhanced away from the band gap in the presence of nonmagnetic interstitial defects. Furthermore, unlike their ferromagnetic counterpart, the TSHE in AFM Sks increases with an increase in the disorder strength, thus opening promising avenues for materials engineering of this effect.