In this paper, we investigate finite amplitude torsional oscillations of a shape-morphing plate submerged in a quiescent, Newtonian, incompressible fluid. To address this problem, we focus on a two-dimensional cross section of the plate and para-metrically study hydrodynamic moments and power dissipation during the plate oscillation as a function of the shape-morphing deformation intensity and the oscillation amplitude. This fluid-structure interaction problem is tackled within the framework of a computational fluid dynamics model where the fluid flow is described via the Navier-Stokes equations and the deformations of the structure are prescribed. The results demonstrate a gradual reduction of hydrodynamic moment and nonmonotonic power dissipation behavior as the imposed shape-morphing becomes more aggressive. In addition, power dissipation can be minimized for an optimum value of the shape-morphing intensity. Results from this study are relevant in underwater systems subjected to torsional oscillations and demonstrate an avenue for hydrodynamic moment control and reduction of energy losses.