To effectively cool blade bases and segment chips and to discharge chips smoothly by ejecting the total amount of cooling medium supplied around the segment chips through a passage formed in a spacer.

In a complex cutting blade in which two cutting blades 10 each comprising a blade base 11 with segment chips 12 secured to the outer peripheral surface thereof are stacked with a spacer 20 between them, a passage 25 for a cooling medium is formed in the spacer 20, and the cooling medium is supplied to the passage 25 to cool the blade bases 11 and the segment chips 12.