Provided is a self-sharpening polishing device with magnetorheological flexible polishing pad formed by dynamic magnetic field and polishing method thereof. The device includes a polishing disc revolution mechanism and a multi-magnetic-pole synchronous rotary drive mechanism, the polishing disc revolution mechanism including a transmission shaft motor, a transmission shaft, a transfer disc, an eccentric shaft fixing disc, a cup-shaped polishing disc and a transmission shaft transmission mechanism, the multi-magnetic-pole synchronous rotary drive mechanism including an eccentric spindle, a synchronous rotary drive disc, flexible eccentric rotating shafts, eccentric sleeves, magnetic poles, the eccentric shaft fixing disc, and a spindle motor, etc. The device does not need a circulating device to renew magnetorheological fluid and does not need to renew the magnetorheological fluid during the finishing process; in fact the entire process from rough polishing to precise polishing can be done at one time. The device maintains a consistent workpiece surface and delivers a low cost and very efficient polishing process that is eminently suitable for the planes of optical elements with large diameter; it is also suitable for studying the material removal mechanism of planar optical materials and detecting sub-surface damage, as well as other experimental studies.