Soak a rag in white vinegar and wrap the rag around the spigot where it meets the wall. The white vinegar softens the calcification. Allow the vinegar to work for 20 minutes. While the spigot is soaking in the vinegar, go under the crawl space and turn off the supply valve to the spigot. The supply valve is usually on a tee connector where the spigot supply pipe connects to the house water supply. If you can't find this turnoff valve, shut off the main water supply to the house.
Remove the screws securing the spigot to the foundation with a Phillips screwdriver or nut driver, depending on the screw head. Adjust the jaws of a pipe wrench over the body of the spigot close to the wall. Ask a helper to hold the pipe wrench in place.
Go into the crawl space and find the first coupling nut, closest to the wall, on the water spigot line. Turn the nut counterclockwise with a pipe wrench while your helper continues to hold the spigot outside. Once the coupling nut is loose, ask your helper to pull the spigot assembly away from the wall.
Cut the copper pipe with a pipe cutter, if there is no coupling nut. Some spigot pipes are soldered together. Cut the pipe 12 inches from the wall with the pipe cutter.