A paper roll cutting device comprises a rotating motorized arm (20), provided with a rotation axis (21) fixed in the space, and at least one cutting blade (30) to cut at least a paper stick (100) obtaining said paper rolls connected to the rotating motorized arm (20), wherein the rotation axis (31) of the cutting blade (30) is cyclically movable during the rotation of the motorized arm (20), the distance between the rotation axis (21) of the rotating arm (20) and the rotation axis (31) of the cutting blade (30) being progressively cyclically variable during the rotation of the motorized arm (20) with a minimum distance at the lower point of the rotation trajectory of the cutting blade (30).