The invention relates to the technical field of ultra-precision machining, in particular to a polishing device and method for a variable-stiffness grinding wheel assisted by magneto-rheological jet flow. The polishing device comprises a bottom plate, a sliding guide rail module, a first bearing seat, a guide wheel, a first iron core, a first coil, a workpiece, an iron core support, a second bearing seat base, a second bearing seat, a magneto-rheological elastomer grinding wheel embedded with abrasive particles, a guide pipe, a magneto-rheological polishing solution storage box, a coupler, a motor, a motor support, a second coil, a second iron core, a base, a bolt, a workpiece support, a first shaft, a second shaft, a pump, a nozzle, a pressure sensor and a third coil. Mechanical polishing and magneto-rheological polishing liquid jet flow polishing for controlling the rigidity of the magneto-rheological elastomer grinding wheel embedded with the abrasive particles through the magnetic field are carried out at the same time, and good surface machining quality and machining efficiency are achieved.