A method of oxygen cutting a piece of steel, in which a cutter member (5) is positioned in such a manner that the cutting jet (6) is directed towards a first face of the piece to be cut (1) and a trimmer member (10) is positioned in such a manner that the trimming jet (12) is directed towards a second face, opposite from the first face, towards the outlet point (14) of the oxygen-cutting jet so as to perform trimming simultaneously on the cutting bead as it forms on said second face, with the positioning of the cutter and trimmer members (5, 10) being such that the cutting jet (6) is applied to the top face (1.1) of the piece (1) in a substantially vertical direction, while the trimming jet (12) is applied to the bottom face (1.2) of said piece in an oblique direction that remains pointing towards the outlet point (14) of the cutting jet (6), simultaneous cutting and trimming being performed by moving the cutter and trimmer members (5, 10) horizontally in synchronous manner, wherein a sprayer member (11) is positioned beneath the piece (1) in such a manner that a fluid jet (13) is sprayed during the cutting process towards the molten particles ejected by the cutting jet (6) so as to reduce fume emission, wherein the sprayer member (11) is carried by the support (20) for the trimmer member (10) passing through the cut slot (1.3).