Close the shut-off valve on the faucet’s water line inside the house. Turn the shut-off handle completely clockwise. Turn on the faucet, if possible, to release any water pressure.
Remove the screw holding the faucet handle in place and pull off the handle. Spray penetrating lubricant on all sides of the nut that sat behind the faucet’s handle and allow the lubricant to soak into the nut’s threads for a few minutes.
Clamp an adjustable wrench to the nut and turn counterclockwise. If the nut won't turn, try tightening it by turning clockwise slightly, which may break apart any corrosion between the nut and the faucet.
Strike the side of the nut with a hammer in an attempt to jar loose the corrosion or any buildup sitting in the threads. Heat up the nut with a hair dryer for five minutes or more if the nut still doesn't turn counterclockwise. The heat makes the nut expand, potentially loosening it enough to unthread from the faucet.
Cut the nut on either side using a close-quarters hacksaw, then remove the nut. Once you remove the nut, pull on the faucet spout to remove the valve stem assembly from the water pipe.