The invention relates to a device for oxyacetylene-cutting pieces of steel. The cutting (5) and deburring mechanisms are positioned in such a way that the oxyacetylene cutting jet (6) acts on the top surface (1.1) of the piece (1) in an essentially vertical direction while the deburring jet (12) acts on the bottom surface (1.2) of said piece in an oblique direction, remaining pointed towards the exit point (14) of the oxyacetylene cutting jet (6). The simultaneous cutting and deburring is made possible by the synchronous horizontal displacement of the cutting (5) and deburring (10) mechanisms. A spraying mechanism (11) is also provided for spraying fluid in the direction of the particles in fusion during the cutting process in order to reduce emissions of fumes.