Device for cutting tubular pieces by means of cutting-wheels, characterized in that two cutting-wheels are disposed symmetrically on either side of the piece to be cut, a pair of lever arms each supporting one of said cutting-wheels being pivoted separately to a shaft rigid with the frame structure of a machine, and that common pressure means acting directly on said lever arms are provided for causing said cutting-wheels to penetrate into the piece to be cut while mutually compensating the pressure reactions of said wheels.