Shut off the main water valve by turning the ball valve handle on the main line clockwise.
Mark the pipe with the old stop about 3 inches below the end of the stop with a marker.
Cut off the pipe on the mark using a hacksaw.
Rub a fine-grit sandpaper around the end of the cut pipe to remove any burrs. On copper pipes, rub the sides of the pipe near the end until the copper shines. This will provide a clean surface for the new fitting.
Place a push-to-fit stop on the end of the pipe. Press down hard on the fitting until it won't go down any farther. The compression ring inside the fitting will automatically create a watertight, pressure-tested seal.
Turn on the main water by turning the ball valve counterclockwise.