This is a cutter assembly for linerless strip media having an uncovered adhesive backing. There is a cutter mounted for transverse movement across the media and a backing bar with at least two cutting edges. The backing bar can be rotated to place one of the cutting edges in position to cooperate with the cutter to cut the media. The backing bar is rotatable about a transverse axis simultaneously with feed movement of the media at a rotational speed equal to the feed speed of the media. This causes the media to ride up on a pointed portion of a cutting edge without dragging across the cutting edge as the cutting edge moves into a use position in which the media is supported by a support surface of the cutting edge. A cleaning station cleans the previously used cutting edge as the bar is rotated. Rotating and fixed cutters can be used. The cutter is replaceable and can be supplied in combination with an associated media for which it is designed. The cutter may partially cut the media to make it separate without fouling the cutter with adhesive. A self-healing "solid" roller is also disclosed.