A cutting device (1), in particular for rapidly cutting webs, comprising: a support structure (2) comprising a fixed blade (3), a carriage (4) movable along a movement direction (X), a mobile blade (5) mounted on the carriage (4), a guide (7), associated to the support structure (2), on which the carriage (4) is slidable along the movement direction (X); a sliding sleeve (11), interposed between the carriage (4) and the guide (7) concentrically to the guide (7); seal means (8, 10) interposed between the guide (7) and the carriage (4) so as to define a chamber (9), concentric to the guide (7) and containing the sleeve (11); motor means (6) configured to move the carriage (4) according to an alternating movement along the movement direction (X) between a non-operating position and an operating position, in which the mobile blade (5) partially superposes the fixed blade (3) so as to carry out the cutting of a web; supply means (15) for supplying air to the chamber (9) so as to maintain it at a greater pressure with respect to the surrounding environment.