Apparatus for laser or plasma cutting of pieces (P) from laminar material wound in coil, comprising: - a cutting station , provided with at least one laser or plasma cutting head movable within an operative cutting area , which is placed downstream of an entrance of the laminar material in said station along a longitudinal advancing direction (X) of said material and is made above a receiving cavity of the cutting swarf (T) of the laminar material; - means for positioning a portion of said laminar material in said operating area on a cutting plane (m) placed on top of said receiving cavity , wherein said positioning means are suitable to maintain said portion of laminar material (M) blocked on said cutting plane (m) during the cutting operations, suspended in the air and longitudinally stretched over said receiving cavity ; and - an electronic control unit in charge of controlling the operation of said apparatus ; wherein it comprises at least one movable device for selective collection of the machined pieces (P), wherein said movable device defines a continuous collection surface and is movable under the cutting plane (m) and parallel to it between an active position, wherein said collection device is positioned inside said operative cutting area closing the receiving cavity between the cutting plane (m) and the bottom of said cavity , and a passive position, wherein said collection device is positioned outside said operative cutting area outside the receiving cavity , and wherein said electronic control unit is programmed to control the movement of said movable collection device between said active position and said passive position in coordination with the execution of the cutting operations, in such a way that that said movable collection device is in the passive position when the cutting head is performing cutting operations that generate swarf (T), in order to leave said swarf free to fall by gravity inside the receiving cavity , and it is instead in the active position, when the cutting head is performing cutting operations which lead to the complete detachment of the pieces (P) from the skeleton (S) so that the pieces (P) are collected by the movable device separately from the swarf (T) and from the skeleton, which is retained by positioning means on the cutting plane (m) above said movable device , characterized in that said movable device consists of a first conveyor belt, having an extension in length such as to project outwards from said cutting station when the movable device is in said active position, wherein said first conveyor belt may be operated in rotation to continuously extract from the operative cutting area the machined pieces (P) that progressively fall on it. - a cutting station , provided with at least one laser or plasma cutting head movable within an operative cutting area , which is placed downstream of an entrance of the laminar material in said station along a longitudinal advancing direction (X) of said material and is made above a receiving cavity of the cutting swarf (T) of the laminar material; - means for positioning a portion of said laminar material in said operating area on a cutting plane (m) placed on top of said receiving cavity , wherein said positioning means are suitable to maintain said portion of laminar material (M) blocked on said cutting plane (m) during the cutting operations, suspended in the air and longitudinally stretched over said receiving cavity ; and - an electronic control unit in charge of controlling the operation of said apparatus ; <EOS>