First, score the circle, making sure that you start and stop the score line at the same point.
Turn the glass over onto a piece of corrugated cardboard, or other surface with some give, with the score line face down. With your thumbs, press along the score line until you see the score line "run" progressively and completely around the circle. This prevents the relief scores you are going to make from running through the circle.
Turn the glass back over to the side on which you scored it. Score several lines perpendicular to the circle to the corners of the piece of glass.
Gently open these scores by tapping with the ball of your cutter, or with your hands, pliers, or other tools. The pieces should fall cleanly from the circle leaving you with no rough or jagged edges.