Cutting circular corners in beveled mat I have a silk-screen print on a square sheet of paper.  The corners of the printed area are arcs with about a one inch radius.

I would like to cut a beveled mat for this print with the opening about a half inch larger than the print area, but I cannot come up with a way to cut the corners.  

If I were making a non-beveled mat, I would use a compass with a blade to make the cut, probably making multiple cuts to make it all the way through the mat. I would cut the arcs first, then join them with straight cuts.

One way to do the beveled arc would be freehand, following a drawn curve, but I know that I don't have the steadiness to pull this off, certainly not so that all four corners would be identical.

Another way would be to use a compass as mentioned above, and arrange the swing leg so that it doubles back to cut at a 45 degree angle, but for it to work it would have to be done in one pass. (If done in multiple passes, each pass would be a slightly different angle, or some magic adjustment would have to be made for each pass.)

For the straight cuts, I have a Logan beveled mat cutter. (in the old days I just made multiple cuts holding the knife a 45 degree angle - of course being freehand after the first pass, each cut was at a slightly different angle from the previous and the results were not always pretty.)

I am hoping there is some way to cut the corner arcs with a device that would produce clean bevels like I get from my straight line bevel cutter.

Does someone know how to do this?
They actually make tools for this. They're called circle cutters. Some of them have the option to do a beveled opening. They're designed to make full circles or ovals but I'm sure you could use them for partial ones, too.

As an example this one has excellent reviews on Amazon and is made by the same company as your straight mat cutter but it looks like it may not be small enough as the minimum circle diameter is 4-3/4 inches and you said you wanted a 2 inch diameter circle.

Here's an example of a mat cut with this cutter:



Hopefully you'd be able to find a similar product with a smaller diameter.