  We report simultaneous Raman sideband cooling of a single $^{87}$Rb atom and
a single $^{133}$Cs atom held in separate optical tweezers at 814\,nm and
938\,nm, respectively. Starting from outside the Lamb-Dicke regime, after
45\,ms of cooling we measure probabilities to occupy the three-dimensional
motional ground state of 0.86$^{+0.03}_{-0.04}$ for Rb and
0.95$^{+0.03}_{-0.04}$ for Cs. Our setup overlaps the Raman laser beams used to
cool Rb and Cs, reducing hardware requirements by sharing equipment along the
same beam path. The cooling protocol is scalable, and we demonstrate cooling of
single Rb atoms in an array of four tweezers. After motional ground-state
cooling, a 938\,nm tweezer is translated to overlap with a 814\,nm tweezer so
that a single Rb and a single Cs atom can be transferred into a common 1064\,nm
trap. By minimising the heating during the merging and transfer, we prepare the
atoms in the relative motional ground state with an efficiency of
0.81$^{+0.08}_{-0.08}$. This is a crucial step towards the formation of single
RbCs molecules confined in optical tweezer arrays.
