Abstract: This invention relates to devices for sawing hard material such as stone, and includes extenders to be affixed to the peripheral surfaces of a sawing core. Each has vertical sidewalls which are spaced-apart from each other by top and bottom spacer elements. The cavity created thereby opens to the front (i.e., in the direction of travel of the core when in use) and to the rear of the extender. The bottom of the cavity, which is formed by the upper surface of the bottom spacer element, inclines upward toward the rear to deflect water that has been sprayed onto the device to lubricate, cool and clean it, onto the next succeeding extenders and their associated cutting surfaces. The top spacer element receives a slideably replaceable cutting member base from said front direction, that may have a U-shaped mounting base and has a matrix element affixed to its top that is adapted to provide desired cutting surfaces.