In the rust removal process via ultra-high-pressure (henceforth UHP) water jet, nozzle translation and rotation significantly affect the jet profile, thereby influencing rust removal performance. Unfortunately, the research on UHP water jets in motion is still rare, lacking systematic theoretical analysis. To address this, 3D numerical simulations incorporating cavitation effect, multiphase flow, and liquid compressibility are conducted to investigate the hydrodynamic performance of UHP water jetting under different translational speeds. The water-jet hydrodynamic characteristics under stationary and translating nozzle conditions are compared in terms of velocity, vortex structure, turbulent kinetic energy, pressure distribution, and impact area. Furthermore, five cases related to different translational speeds are analyzed to examine the influence of motion on jet behavior. Results show that the stationary jets exhibit axisymmetric velocity profiles and vortex structures. When the translational motion is introduced, the jet deflects opposite to the nozzle movement, triggering enhanced shear layer instability. This kind instability serves as a primary driver for the emergences of increased turbulence, vortex deformation, and pressure asymmetry. Consequently, the turbulent kinetic energy distribution broadens and decays more rapidly downstream. Pressure distributions become asymmetric, with high-pressure zones forming upstream and more intense pressure decaying downstream. The effective impact area expands significantly under moderate wall-shear-stress thresholds, but becomes less uniform at higher velocities. An optimal translational speed of approximately 20 m/s can be identified, offering the best trade-off between cleaning performance and energy efficiency. This study provides theoretical support and practical guidance for advancing rust removal technology via UHP water jetting.