The present invention provides a fixed abrasive grain wire saw and a method for dressing a fixed abrasive grain wire which carries out a reasonable design after considering an operating aspect such as maintenance and repair for an arrangement relationship between a worktable to maintain a work and a dressing stone to dress a fixed abrasive grain wire. The fixed abrasive grain wire saw comprises: a fixed abrasive grain wire (2); a work supply table (6) having a work fixing unit (15) on which a work (W) is fixed; and a dressing stone (41). The fixed abrasive grain wire (2) is wound between groove rollers (3-5) to form a wire row (30) arranged along the groove rollers in a transport direction. The dressing tone is arranged adjacent to the work fixing unit and fixed on a position of an upstream side from the work fixing unit of the transport direction in the work supply table.