Mug mats are very popular and you can easily make one using an applique rectangle like this one.

Hoop a water-soluble fabric type stabilizer and run the first stitch - the placement stitch.

Remove the hoop from the machine and add a layer of felt or dense batting and the backing fabric on the back. Tape and pin it in place. Place the front fabric in the front of the hoop and put the hoop back on the machine.

Run the second stitch, the tackdown stitch, to tack everything in place.