A method for managing machining dust during laser machining of a workpiece, said method comprising the steps of: (i) providing a laser machining device comprising: - a laser source; - a machining support comprising a top end and a bottom end; for receiving and supporting a workpiece by the application of a force directed from said bottom end toward said top end; - an optical system for directing a laser beam generated by said laser source toward said machining support, according to one or more attack trajectories, each of said one or more attack trajectories being characterized by a vector AB ⇀ directed at least partially from said top end toward said bottom end; - generating means for generating a gas stream; - directing means for directing said gas stream toward a zone lying above said machining support; - recovery means for recovering at least part of said gas; (ii) placing said workpiece on said machining support; (iii) activating said laser source for generating said laser beam; (iv) directing said laser beam by means of said optical system toward said machining support, according to said one or more attack trajectories; (v) activating said generating means to generate said gas stream; (vi) directing said gas stream by means of said directing means, toward said zone lying above said machining support; (vii) recovering at least said part of said gas by means of the recovery means; characterized in that - said directing means are configured to direct said gas stream along a main trajectory characterized, above said machining support, by a vector v ⇀ directed partially from said bottom end toward said top end, to create a suction effect able to entrain a gas away from said machining support; - said gas stream is directed in step (vi) along said main trajectory, above said workpiece, to create said suction effect, to entrain said gas away from said machining support. (i) providing a laser machining device comprising: - a laser source; - a machining support comprising a top end and a bottom end; for receiving and supporting a workpiece by the application of a force directed from said bottom end toward said top end; - an optical system for directing a laser beam generated by said laser source toward said machining support, according to one or more attack trajectories, each of said one or more attack trajectories being characterized by a vector AB ⇀ directed at least partially from said top end toward said bottom end; - generating means for generating a gas stream; - directing means for directing said gas stream toward a zone lying above said machining support; - recovery means for recovering at least part of said gas; - a laser source; - a machining support comprising a top end and a bottom end; for receiving and supporting a workpiece by the application of a force directed from said bottom end toward said top end; - an optical system for directing a laser beam generated by said laser source toward said machining support, according to one or more attack trajectories, each of said one or more attack trajectories being characterized by a vector AB ⇀ directed at least partially from said top end toward said bottom end; - generating means for generating a gas stream; - directing means for directing said gas stream toward a zone lying above said machining support; - recovery means for recovering at least part of said gas; (ii) placing said workpiece on said machining support; (iii) activating said laser source for generating said laser beam; (iv) directing said laser beam by means of said optical system toward said machining support, according to said one or more attack trajectories; (v) activating said generating means to generate said gas stream; (vi) directing said gas stream by means of said directing means, toward said zone lying above said machining support; by means of said directing means, toward said zone lying above said machining support; (vii) recovering at least said part of said gas by means of the recovery means; - said directing means are configured to direct said gas stream along a main trajectory characterized, above said machining support, by a vector v ⇀ directed partially from said bottom end toward said top end, to create a suction effect able to entrain a gas away from said machining support; - said gas stream is directed in step (vi) along said main trajectory, above said workpiece, to create said suction effect, to entrain said gas away from said machining support.