The invention discloses a hot melting damping fin punching and cutting device and a punching method thereof, and belongs to the technical field of vehicle damping. The hot melting damping fin punching and cutting device comprises a punching and cutting device body, and a special conveying belt penetrating through the punching and cutting device body for conveying hot melting damping fins, wherein the punching and cutting device body comprises two support tables on two sides of the special conveying belt, punching tables flatly placed and fixed on the side surfaces of the two support tables, and lifting height adjusting mechanisms; and the punching tables are connected with cutter molds detachably mounted at the bottoms of the punching tables through the lifting height adjusting mechanisms. The punching heights and thicknesses of the cutter molds are adaptively adjusted through the lifting height adjusting mechanisms; and after the hot melting damping fins are effected, the lifting travels can be shortened, and the damage of the conveying belt due to excessive punching is prevented. The device solves the problems of bad burrs in cutting of the damping fins and short service life of the conveying belt.