I have had very good luck cutting circles in vinyl and tape
I use a drafting quality set of dividers (the compass you never use cause there are points at both ends).
You can carefully 'cut' the material with several gentle passes of the dividers.
If a pin hole in the middle is not to your liking, I use one of those peel and stick rubber protective "feet" that typically protect table tops from being scratched or sometimes straighten delinquent pictures hanging cockeyed on the wall.