Near the minor axis of the Galactic bulge, at latitudes b < -5degrees, the red giant clump stars are split into two components along the line of sight. We investigate this split using the three fields from the ARGOS survey that lie on the minor axis at (l, b) = (0degrees, -5degrees), (0degrees, -7degrees5), (0degrees, -10degrees). The separation is evident for stars with Fe/H > -0.5 in the two higher-latitude fields, but not in the field at b = -5degrees. Stars with Fe/H < -0.5 do not show the split. We compare the spatial distribution and kinematics of the clump stars with predictions from an evolutionary N-body model of a bulge that grew from a disk via bar-related instabilities. The density distribution of the peanut-shaped model is depressed near its minor axis. This produces a bimodal distribution of stars along the line of sight through the bulge near its minor axis, very much as seen in our observations. The observed and modeled kinematics of the two groups of stars are also similar. We conclude that the split red clump of the bulge is probably a generic feature of boxy/peanut bulges that grew from disks, and that the disk from which the bulge grew had relatively few stars with Fe/H < -0.5.