The invention relates to the technical field of material cutting, and provides a flexible material cutting device. The flexible material cutting device comprises a base, a first elastic mat, a second elastic mat, a cutter and an upper pressing base; the upper pressing base is located at the corresponding position above the first elastic mat and the second elastic mat and is provided with a first compression part and a second compression part used for pressing a flexible material, at least two protruding parts facing the base are arranged on the face, facing the base, of the first compression part, and the top ends of the protruding parts are gradually and upwards distributed in a heightening manner in the slantly-upward direction from the side edge of the side, far away from the second compression part, of the upper pressing base to the middle portion; and at least two protruding parts facing the base are arranged on the face, facing the base, of the second compression part, and the top ends of the protruding parts are gradually and upwards distributed in a heightening manner in the slantly-upward direction from the side edge of the side, far away from the first compression part, of the upper pressing base to the middle portion. The flexible material cutting device solves the problem that after an existing flexible material cutting device is used for cutting the flexible material, the flexible material is low in quality, and the efficiency is not high.