We demonstrate a continuously tunable, multi-Stokes Raman laser operating in the visible range (420 - 600 nm). Full spectral coverage was achieved by efficiently cascading the Raman shifted output of a tunable, frequency-doubled Ti:Sapphire laser. Using an optimized hemi-spherical external Raman cavity composed only of a diamond crystal and a single reflecting mirror, producing high power output at high conversion efficiency (>60 % from pump to Stokes) for a broad range of wavelengths across the visible. Enhancement of the cascading was achieved by controlling the polarization state of the pump and Stokes orders. The Stokes outputs exhibited a linewidth of 11 ± 1 GHz for each order, resembling the pump laser linewidth, enabling its use for the intended spectroscopic applications. Furthermore, the Raman laser performance was demonstrated by applying it for the resonance excitation of atomic transitions in calcium.