An electronically-controlled apparatus for machining natural or synthetic stone plates or glass plates, comprising: - a supporting structure defining a machine top for receiving the plates to be machined, - a machining head movable above the machine top in at least two mutually orthogonal directions (X, Y, Z) and provided with a machining tool, - an electronic control unit, programmable to control said machining head according to a predetermined machining cycle, - wherein said machine top includes a plurality of units for supporting and holding the plate to be machined, each supporting and holding unit being switchable between an active holding condition and an inactive condition, - wherein each of said supporting and holding units is movable along a first horizontal direction over a respective support cross-member - wherein each cross-member is movable on the machine top in a second horizontal direction perpendicular to said first horizontal direction, characterized in that said electronic control unit is programmed to perform a machining cycle which includes the following operations: - positioning a plurality of supporting and holding units which are selected to receive a plate (L1, L2) thereon, by arranging all selected units on the two sides of a cutting line, which must be followed when cutting said plate (L1, L2), - activating said supporting and holding units in such a way as to clamp the plate (L1, L2) thereon, - providing said machining head with a cutting tool and controlling the machining head for cutting said plate (L1, L2) along said cutting line, - maintaining said supporting and holding units in the active holding condition and spacing apart the plate portions (L1A, L1B, L2A, L2B) from each other, which have been subdivided from said plate (L1, L2), by means of: - a movement along said second horizontal direction of the cross-members carrying at least some of said selected units, and/or - a movement of at least some of said selected units along said first horizontal direction, - providing said machining head with a tool for machining the edges of said plate portions, and controlling the machining head for machining the edges of said plate portions, while maintaining said selected supporting and holding units active, whereby said apparatus is able to perform both the plate (L1, L2)-cutting operations and machining operations of the edges of the plate portions (L1A, L1B, L2A, L2B) obtained as a result of the cutting operation, without the need to arrange a sacrificial plane above the machine top to perform a cutting operation. - a supporting structure defining a machine top for receiving the plates to be machined, - a machining head movable above the machine top in at least two mutually orthogonal directions (X, Y, Z) and provided with a machining tool, - an electronic control unit, programmable to control said machining head according to a predetermined machining cycle, - wherein said machine top includes a plurality of units for supporting and holding the plate to be machined, each supporting and holding unit being switchable between an active holding condition and an inactive condition, - wherein each of said supporting and holding units is movable along a first horizontal direction over a respective support cross-member - wherein each cross-member is movable on the machine top in a second horizontal direction perpendicular to said first horizontal direction, - positioning a plurality of supporting and holding units which are selected to receive a plate (L1, L2) thereon, by arranging all selected units on the two sides of a cutting line, which must be followed when cutting said plate (L1, L2), - activating said supporting and holding units in such a way as to clamp the plate (L1, L2) thereon, - providing said machining head with a cutting tool and controlling the machining head for cutting said plate (L1, L2) along said cutting line, - maintaining said supporting and holding units in the active holding condition and spacing apart the plate portions (L1A, L1B, L2A, L2B) from each other, which have been subdivided from said plate (L1, L2), by means of: - a movement along said second horizontal direction of the cross-members carrying at least some of said selected units, and/or - a movement of at least some of said selected units along said first horizontal direction, - a movement along said second horizontal direction of the cross-members carrying at least some of said selected units, and/or - a movement of at least some of said selected units along said first horizontal direction, - providing said machining head with a tool for machining the edges of said plate portions, and controlling the machining head for machining the edges of said plate portions, while maintaining said selected supporting and holding units active,