Plastic bottles are easy to cut with a sharp scissors.
Before cutting your circle, draw your cutting line onto the bottle with a marker.
Before you can cut with a scissors, you have to pierce the plastic with a stiletto or knife. That piercing will be messy, so pierce in the center of your marked circle. UseThen use the scissors to cut from the center to the marked edge of the circle.
Because your circle is so small, use a small scissors or manicure scissors. Cut counter-clockwise around the circle (unless you are a lefty).