Plumbing is hard work. Pipes heat up and cool down and are inherently wet, which leads to corrosion, which causes stuck pipe joints. Rather than grab a bigger hammer or a hacksaw and risk causing more damage, approach the situation calmly and apply logic. Cast iron and steel pipe has threaded joints, which will turn loose if you can twist them. Copper and PVC pipes have permanently soldered and chemically glued joints that must be cut out and worked around.
Position yourself where you can get a good grip on the pipe. Adjust any needed light to focus on the part of the pipe you are working on. Spray aerosol penetrating oil into the joint around the pipe and let it work for a full minute.
Position your pipe wrench on the pipe, down-line from the joint you need to get loose. Tilt the handle so that you have plenty of room to push or pull it to turn the pipe counterclockwise. Close the wrench until it grips the pipe firmly.
Grasp the handle of the pipe wrench in both hands and move it to turn the pipe in a counterclockwise position. Slip a length of pipe over the wrench handle to extend it for extra leverage if it still refuses to move.
Apply heat from a heat gun to the joint for 20 to 30 seconds, then allow it to cool and try the wrench again to break loose stubborn pipes. Continue turning the pipe counterclockwise, shifting the wrench as needed.
Inspect the pipe to determine which side of the pipe joint it will be easier to attach to. Look for space around the pipe to fit joints into and solid pipe that will hold the joints well.
Mark the pipe where you intend to cut it. Make your line around the pipe, as far as possible, keeping it perpendicular to the length of the pipe for a cutting guide line. Wipe any moisture from the pipe with a dry rag.
Drag the blade of a hacksaw across the mark to groove it, cutting into the surface lightly to make a channel for the blade. Start your cut by dragging the blade toward you with light pressure. Push back and forth, keeping the teeth of the blade in contact with the pipe. Keep cutting in a back and forth motion, staying as true to the line as possible until the pipe is cut through.
Sand or file the end of the cut pipe smooth for a good joining surface for the new fitting. Work to get the end as flat as possible for the best joint. Lightly scuff the sides of the pipe near the end with sandpaper for a better join.