Disclosed is an improved precision cutting apparatus comprising a chuck table for holding a workpiece, and first and second cutting means each including a spindle unit having a blade attached thereto. The first and second cutting means are series-arranged with their blades opposing a predetermined distance apart, thereby cutting along two traces at one time by moving the chuck table relative to the stationary cutting means. These cutting means need not be allowed to overrun the workpiece while cutting, thus saving extra time required for overrunning which otherwise, would be required as is the case with the parallel-arrangement of two cutting means, and accordingly the dicing can be performed at an increased efficiency.