An improved structure of a circle-cutting tool has an outer ring seat having a round hollow groove and a placing surface. A rotary disc is pivoted into the round hollow groove of the outer ring seat for rotation in relation to the outer ring seat, and has a top surface, bottom surface, outer ring portion and central portion. An elongated through groove penetrates through the top and bottom surfaces of the rotary disc in an elongated shape. The elongated through groove is set in a way to be extended from the central portion of the rotary disc to the outer ring portion. An adjustable elastic cutting assembly is pivoted into the elongated through groove in a slidable state in relation to the elongated through groove.