The present invention relates to a method of designing, previewing a stone veneer project in its entirety before a single stone is cut; cutting and finishing the edges of a stone to form interconnecting natural stone veneer components, each having a perimeter of a pre-determined contour and a finished edge, the method comprising: drawing or otherwise importing a design plan comprising overall dimensions and shape of a finished stone veneer project; drawing or otherwise importing a pattern of shape and placement of the stone veneer components within the design plan; programming, scanning or otherwise inputting a plurality of cutting patterns, wherein the cutting patterns are the same or different, each cutting pattern designed to form the stone veneer component having a perimeter of a pre-determined contour; converting the pattern into a machine-readable program to produce a cutting path on an abrasive waterjet machine; loading a cutting path file for the stone veneer component into the abrasive water jet machine; positioning a cutting head of the waterjet machine over the natural stone at a distance of from about 0.3 inch to about 4 inches from a contact surface of the stone; running the cutting path program and cutting through the stone by contacting the contact surface of the stone with a waterjet from the waterjet machine.