A method and a cutting system for sheets includes a cutting center, a sorting apparatus with handlers for gripping pieces cut by the cutting center, and a transfer board, movable between the handler area and the inside of the cutting center, supporting the sheets. The cutting center includes a cutting head movably mounted above the transfer board with a distance detection sensor, detecting distance data with respect to a sheet on the transfer board. The cutting center and sorting apparatus have respective first and second control logics. A data interface unit lies between the first and second control logic, by which distance data from the distance detection sensor, are transferred. The second control logic has a processor defining, periodically during operation cycles, an altitude map based on the distance data detected in a number of positions, and controlling a gripping step of the handlers based on the altitude map.