Some experiments have witnessed gradual decoupling of viscosity from the translational self-diffusion of supercooled water with decreasing temperature. This indicates the breakdown of the Stokes-Einstein equation in supercooled water. While some theoretical and computer simulation studies indicated the jump translation of the molecules as a probable origin of the above decoupling, direct quantitative evidence is still lacking. Through a molecular dynamics (MD) simulation study, along with careful consideration of translational jump motion, we have found the most definite proof of increasing relevance of translational jump diffusion in the above decoupling phenomena. By separating the jump-only diffusion contribution from the overall diffusion of the water, we obtain the residual diffusion coefficient, which remains strongly coupled to the viscosity of the medium at the supercooled regime. These new findings can help to elucidate many experimental studies featuring molecular transport properties, where strong diffusion-viscosity decoupling is present.