Turn the shutoff valve beneath the fixture by hand to turn the water off. If there isn't one available near the fixture, turn off the home's water shutoff valve, which is usually located inside the house where the water line enters the home.
Select the correct wrench. A set of Stillson pipe wrenches are most commonly used for loosening pipes -- one for holding the pipe and the other for turning. Choose a closet spud wrench in conjunction with a vise grip wrench to loosen the copper pipe in a tight area. Or select a basin wrench to loosen copper fittings or hose couplings under sinks.
Grip the fittings on the end of the copper pipe in between the teeth of the wrench. Then move the wrench counterclockwise to loosen it. If you can't get a grip on the fitting, hold the pipe in place with a Stillson pipe wrench or vise grip wrench, then turn the fitting. Once fittings are removed, the copper pipe will be loose.
Cut the copper pipe with a small hacksaw or tube cutter, if the fittings can't be removed. Before cutting, grip the pipe with a vise grip wrench. Then place the blade or cutter near the end of the pipe, close to the fitting, and saw or cut it away.