Make sure your groove at the base of the pot is still well-defined. When cutting pots off the mound, use a very flexible line that won't kink the way wires will. I prefer fishing line that is at least 30 pound test, with a preference toward braided line as opposed to monofilament line. By tying an old sewing machine bobbin at one end, I make it easier to keep the line from getting lost among the scrap clay.
As the wheel very slowly rotates, lay the line into the groove, being sure to keep the line parallel to the bat below. Once the line has been laid all the way around the pot, pull the ends in opposite directions so as to cut through the clay.