The device (10) for stacking sheets (40) arranged to form stacks (4) downstream of a sheet cutting line and comprises an unroller, a printer and a cutter (6). The device has a stacking table (20) located in the same plane as an evacuation conveyor (5) and the device includes an unloading conveyor (7) with first and second ends (70, 71). The unloading conveyor (7) is arranged to transfer the cut sheets (40), one by one, from the cutter outfeed conveyor (3) towards the stacking table (20) and is coupled with driving mechanism arranged to move the second end (71) between a low position in which the second end (71) is located at the level of the stacking table (20), and a high position in which the second end (71) is located at a height corresponding to that of the complete stack (4).