An apparatus for cutting slab material comprising a working table to support the slabs to be cut during working; a working unit comprising disk cutting means and water-jet cutting means; and a unit for moving the working unit above the working table. The movement unit comprises a horizontal translation unit to move the working unit along two directions parallel to the working table and perpendicular to each other; a vertical translation unit to move the working unit along a direction perpendicular to the working table; a first rotation unit to rotate the working unit about a first axis, vertical and substantially perpendicular to the working table; and a second rotation unit to rotate the working unit about a second axis, inclined with respect to the first axis. Said disk cutting means and water-jet cutting means are integral and therefore the second rotation unit rotates simultaneously with the said cutting means.