Cryogenic liquid turbine expanders have emerged quite recently as a replacement of J-T valve for enhancing energy efficiency of industrial systems, such as Air Separation Units (ASUs), Supercritical Compressed Air Energy Storage (SC-CAES) systems, et al. In the liquid turbine expander, the rotating impeller-induced swirling flow and cavitation are essentially significant and intensive, which requests some in-depth work towards a thorough understanding flow physics and then effective attenuation. The present study aims at effectively mitigating the swirling flow and cavitation. The entropy production analysis method (EPAM) is proposed to characterize the swirling flow and cavitation. It is then incorporated with the improved cavitation and turbulence models and validated through the simulation of the Hord's liquid nitrogen hydrofoil. To mitigate the swirling flow and subsequent cavitation, the design optimization method is developed, in which a novel optimization objective function is constituted by incorporating the local entropy production rate and vapor volume fraction to capture the mechanical energy dissipation and cryogenic cavitating flow physics; the NURBS-FFD (Non-Uniform Relational B-Splines and Free Form Deformation) parametric method is used to facilitate a flexible variation in impeller blade and diffuser vane geometries. It is solved within CFX frame by means of the Particle Swarm Optimization algorithm coupling the Kriging-based adaptive surrogate model. With the design optimization, the impeller and vaned diffuser tube geometries are collaboratively fine-tuned, and the mechanical energy dissipation and cavitating flow across both the impeller and vaned diffuser tube is effectively mitigated.