Put on protective eye gear.
Clean your mirror of any debris with rubbing alcohol. This is very important because if you neglect to do so, it may cause the mirror to break unevenly where you are trying to cut.
Draw out the circle in the size you want to make it. To get an even circle, attach a washable glass marker to a protractor and draw it onto your mirror.
Using your circular glass cutter, begin to score the glass, applying even pressure. The circular glass cutter has a rubber piece that will attach in the middle of your circle, holding it in place in the center.
Break the mirror where it has been scored over a garbage can. Make sure you have your protective gloves on.
Start sanding the edges with sand paper. Sand in a downward motion. If you sand upward, it may cause pieces to break off, ruining the cut.