A cutting device feeds a web between a die roll and an anvil roll, and cuts a continuous portion of the web. The cutting device includes a continuous portion transport unit configured to hold and transport the continuous portion of the web being continuous in a moving direction of the web, and a discontinuous portion transport unit configured to hold and transport a discontinuous portion of the web being discontinuous in the moving direction of the web. The die roll includes a first large diameter portion whose outer peripheral surface is provided with a cutting blade configured to cut the continuous portion of the web. The anvil roll includes a second large diameter portion disposed to face the first large diameter portion. By the discontinuous portion transport unit, the discontinuous portion passes through between the die roll and the anvil roll without contacting the first large diameter portion and the second large diameter portion.