The evidence of multi-photon absorption enhancement by the dual-wavelength double-pulse laser irradiation in transparent sapphire was demonstrated experimentally and explained theoretically for the first time. Two collinearly combined laser beams with the wavelengths of 1064 nm and 355 nm, inter-pulse delay of 0.1 ns, and pulse duration of 10 ps were used to induce intra-volume modifications in sapphire. The theoretical prediction of using a particular orientation angle of 15 degrees of the half-wave plate for the most efficient absorption of laser irradiation is in good agreement with the experimental data. The new innovative effect of multi-photon absorption enhancement by dual-wavelength double-pulse irradiation allowed utilisation of the laser energy up to four times more efficiently for initiation of internal modifications in sapphire. The new absorption enhancement effect has been used for efficient intra-volume dicing and singulation of transparent sapphire wafers. The dicing speed of 150 mm/s was achieved for the 430 μm thick sapphire wafer by using the laser power of 6.8 W at the repetition rate of 100 kHz. This method opens new opportunities for the manufacturers of the GaN-based light-emitting diodes by fast and precise separation of sapphire substrates.