Cutting circular corners in beveled mat
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.