Average intensity and the normalized powers of the completely polarized and the completely unpolarized portions of a radially polarized twisted Gaussian Schell-model (TGSM) beam propagating in underwater turbulence are examined. In our formulation, our previously obtained atmospheric turbulence solution for the same radially polarized TGSM beam using the extended Huygens-Fresnel principle is utilized, with the inclusion of our recently derived expression for the atmospheric turbulence structure constant in terms of underwater turbulence parameters. Effects of the rate of dissipation of mean-squared temperature, rate of dissipation of kinetic energy per unit mass of fluid, kinematic viscosity, and the contribution of the temperature-to-salinity ratio to the refractive index spectrum on the average intensity, and the normalized powers of the completely polarized and completely unpolarized portions of a radially polarized TGSM beam propagating in underwater turbulence are presented.