The invention discloses a floating polisher and a polishing method. The floating polisher comprises a base, a supporting seat, an angle grinder, a fixed support and a connecting rod mechanism. The connecting rod mechanism comprises two parallel connecting rods, and a thin cylinder assembly is arranged between the two connecting rods. During work, a robot grabs a workpiece to enable the workpiece to approach the angle grinder. When the workpiece is in contact with the angle grinder, the angle grinder is subjected to external force exerted by the workpiece, the external force is transferred to a piston rod of a cylinder through the connecting rod mechanism, the piston rod is pulled out, and the angle grinder starts polishing the workpiece with certain floating quantity. After polishing is finished, the robot moves the workpiece away, the external force is eliminated, pressure difference is generated at the two ends of a cylinder piston, the piston rod generates pulling force, and the polisher is pulled to an initial position through the connecting rod mechanism. The floating polisher can achieve parallel floating by means of the connecting rod mechanism, floating and resetting can be achieved through the cylinder, flexible contact between the polisher and the workpiece is achieved, the service life of the polisher is prolonged, and automation of work of casting cleaning and the like is achieved.