A cured-concrete-cutting saw which is sufficiently mobile as facilitates its transport to a work site located within a building, and between work sites within a building, for example, and which is useful in cutting block-out grooves for expansion joints between adjacent sides of adjacent concrete slabs and/or troughs in the surface of such slabs. The saw includes a housing, a blade assembly comprising a plurality of circular blades disposed in spaced apart parallel relationship to one another on the outboard end of a driven shaft that is mounted on the bottom of the housing. A motor provides power for rotation of the shaft and its blade assembly. Optionally, the motor provides power for propelling the saw over the top surface of a concrete slab. A mechanism is provided for operator adjustment of the depth of cut of the blades of the blade assembly from a position adjacent the aft end of the saw. Through the means of selecting different diameter blades for the blade assembly, the saw may be employed to cut a variety of block-outs or troughs of different cross-sectional geometries, in the top surface of a concrete slab. A method is disclosed for the formation of an elongated block-out or trough in the top surface of a cured concrete slab for the preparation of adjacent side margins of adjacent sides of adjacent concrete slabs and for the installation of an expansion strip in the space between these adjacent sides.