The present invention relates to a cutting device comprising a manual gripping element (100) and a cutting assembly (200) that is positioned on one end of the gripping element (100) and comprises a punch (210) split into at least two cutting tips (220, 230), at least one of these tips (220, 230) being hinged on the gripping element (100) in order to be movable between a rest and cutting position in which the tips (220, 230) are adjacent and a working and injection position in which the tips (220, 230) are spaced apart, and urging means (250) designed to move each movable tip (220, 230) into the working position when these urging means (250) press against the skin.