PURPOSE: To make a round cutter follow cords so as to cut a band-like rubber member easily by a method and a device wherein a part of the band-like rubber member floating in the air in a mounted state is cut by the round cutter, which is movable rectangularly with respect to the running direction, running with rotation.

CONSTITUTION: When a rubber sheet 1 is conveyed for a predetermined quantity and stopped, support rollers 60, 61 go up and raise the sheet 1 so as to form a mounted part 1a. Rubber pressers 64b, 65b at upstream and downstream sides are protruded so as to press the sheet 1, so that the part 1a is pulled to both sides so as to be tensioned. Here, when a round cutter 30 is lowered, the edge of the blade bites a predetermined position of the sheet 1 accurately and pulls in the outer skin of the sheet 1 with the V-shaped edge. Steel cords 2 embedded in the sheet 1 floating in the air in a mounted state move easily so as to evade the cutter. The edge bites a space formed with a neighboring cord 2 so as to cut the biting part by providing a cutter receive plate 71 on the bottom face of the bitten part 1a, so that the blade edge penetrates the bottom face of the sheet 1, thereby cutting the sheet.