A cutter employing flat replaceable blades and providing a handle and support memeber that is shaped as an annular segment cut off by a planar surface. The blade is held by a shaft which is preferably encircled by a sleeve and locked to it against rotation. The shaft alone or both the shaft and sleeve extend through a horizontal opening parallel to the planar surface and are locked in place at any desired rotational position. The shaft provides a blade-holding channel enabling ready adjustment of the cutting depth of the blade. In addition to straight cuts and freehand cuts, the latter may be used for circular cuts by attaching a radius rod to it. Cuts of limited length can be simplified by use of another attachment. A further attachment is used to make cuts parallel to the edge of the mounting board.