  We show that a Skyrmion in a classical bipartite antiferromagnetic lattice
can be spatially displaced in a controlled manner by externally applied spin
waves. We reveal the relation between the Skyrmion motion and the spin wave
properties. To this end, we derive a classical spin wave formalism which is
tailored to the antiferromagnetic two-dimensional square lattice. The
antiferromagnetic spin waves can be classified into two types with respect to
their polarization, with two modes each. The circularly polarized spin waves
oscillate with different amplitudes in the respective sublattices and induce a
Skyrmion Hall effect. The two modes are symmetric under sublattices exchange
and determine the overall sign of the Hall angle. Linearly polarized spin waves
oscillate elliptically, however, with the same amplitude on each sublattice.
These accelerate the Skyrmion solely into their own propagation direction. The
two modes are symmetric under component x-y exchange and impact Bloch- or
N\'eel Skyrmions differently. Our results indicate possible technical
applications of spin-wave driven Skyrmion motion. As one example we propose a
racetrack where spin waves pump Skyrmions along the track in antiferromagnets.
