That will leave thick edges. Another option is to place the front and back WST (wrong sides together) and then a satin stitch around the edge. Make a sample first to get the width setting wide enough to cover the edges.
A wave stitch works too if you have a serger.
You can also cut the backing fabric larger than the mug rug. Maybe 2 inches works. Then double fold and stitch down on the front. Easy to miter the borders.