The machine for cutting leathers comprises: a bearing structure (1), an operating element (2), shaped in such a way as to exhibit a rotation axis (Z) and at least three distinct work planes (21, 22, 23), each of which is arranged about the rotation axis (Z) and is provided with an aspirating plate that is activatable/deactivatable such as to retain or release the leathers, and cutting means (3) associated to the bearing structure (1), at a relative side thereof, and movable with respect thereto. The operating element (2) is mountable on the bearing structure (1) rotatably about its rotation axis (Z) and is activatable in rotation about the axis (Z) in order to successively position each work plane (21, 22, 23) at three successive and distinct positions (P1, P2, P3) with respect to the bearing structure (1): a first position (P1) of placing the leathers in which the leathers can be positioned and stretched above the work plane (21, 22, 23) and held stretched thereon following activation of the relative aspirating plate; a second position (P2) of cutting the leathers, in which the work plane (21, 22, 23) with the leathers stretched and retained thereon by the relative aspirating plate is located below the cutting means (3); a third position (P3) of unloading the leathers, wherein the leathers can be unloaded from the work plane (21, 22, 23) by force of gravity following the deactivation of the aspirating plate.