© 2018 American Chemical Society. We present an extensive first-principles time-dependent density-functional theory study of the optical response of small (M/M′)6and (M)3(M′)3six-atom clusters (unary and equimolar binary hexamers of group IB metals: Cu, Ag, and Au), both in the gas-phase and supported on the MgO(100) surface, chosen as a model of a simple oxide substrate. UV-vis spectra are predicted and analyzed in detail in terms of ground- and excited-state wave functions and the involved Kohn-Sham orbitals, to rationalize origin and features of optical absorption in these systems. The interaction with the surface, in particular with the electric field generated by the charge-separated substrate, is found to induce a fragmentation and a shift toward lower energies of the absorption peaks, which is in tune with available experimental information and can be beneficial in terms of applications of these systems as photoenhancers or promoters. The orientation of the transition dipole moment with respect to the support (whether parallel or perpendicular) is also analyzed as a key parameter to translate the present result to noninert supports to tune and optimize oscillator strengths and interaction with substrate excitations.