Three-dimensional potential energy functions (PEFs) have been generated for the X-3 Sigma(g)(-), a(1) Delta(g), b(1) Sigma(g)(+), and c(1) Sigma(u)(-) states of CS2++ using internally contracted multi-reference configuration interaction approach. The analytic forms of the PEFs have been employed in the calculations of the vibrational energy levels, the wave functions, and the Franck-Condon factors for the direct ionization process CS2-->CS2+++2e. As in CS2 and CS2+, strong anharmonic resonances are found in all four states. The spectra are predicted to consist of vibrational progressions of Fermi polyads. For the (1) Delta(g) state the Renner-Teller problem has been solved and the pattern of the bending levels has been analyzed. For 14 electronic states one-dimensional collinear cuts along the charge separation path CS++S+ have been calculated and the corresponding barrier heights of the predissociating states have been determined. The experimental onset for the charge separation paths CS2++-->CS++S+ at about 30 eV is found to be consistent with the calculated barrier height on the PEF of the X-3 Sigma(g)(-) state.