I’ve had good luck using a belt sander to resurface those disc
cutters. If you have a new belt, say a medium grit, and hold the
bottom of the cutter against the rotating belt, turning the cutter as
you work, you can get a flat surface back on your disc cutters. Take
care not to get the cutters hot while grinding, and keep the cutter
rotating while you grind to keep the bottom perpendicular to the
punch. Any bur generated on the edge of the cutter by the grinding
will need to be carefully removed with a sanding stick afterwards,
say a 400 grit.
Those cutters are not terribly sophisticated devices. As long as the
edges are sharp and the outside diameter fits within the cutter die,
they seem to cut just fine.
And yes, most issues with these cutters seem to be from people using
them wrong side up, trying to cut an impossibly thick material with
them, or using a steel punch to remove them from the die. ( we use a
small wooden dowel and a mallet to drive the cutters out of the die
And I’d like to take a moment to sing the praises of belt sanders!