This pipe twisted and severed when I was trying to unsrew an old outdoor faucet. It's about 1.5" (4 cm) deep in the exterior hole. I can grip the pipe with needle-nose pliers, but I can't move it.
How would I go about removing the pipe, ideally leaving the pipe fitting into which I would screw a new outdoor faucet?
The exterior siding is vinyl over insulation. On the interior side is a finished room with drywall. If it is necessary to cut into one of these sides, I'm curious which would be recommended (I think I'm leaning interior).
I am comfortable with basically every handyman task except plumbing; but in this case, because this pipe has a dedicated shut-off valve, I figure it's worth giving a shot. However, I also don't have many plumbing-specific tools. If soldering is necessary, I will call in a professional.
Update: I cut a hole in the interior wall to take a look, and the pipe is soldered. Other houses in the neighborhood, built in the same year, have threaded fittings, but alas. I taped over both holes and called a professional to take care of the rest.
I will come back and describe the plumber's solution for completeness. 
Final Update: The plumber cut the pipe at the vertical section, then soldered a small section of pipe to extend it to the previous height, then soldered an elbow onto that, and finally inserted a hydrant from the exterior and soldered that into the elbow. The hydrant is flush with the exterior and caulked.
Cost was 300 USD, but we have a dry foundation and I didn't burn the house down learning to solder copper pipe. I'm going to install an access panel instead of repairing drywall, per a suggestion in the comments. Thanks!
Best Answer
Interior is the side to cut in your case, and you will need to get into the wall to remove/replace the piping and hose bib. Simplest terms: you limit exposure to the elements/pests/etc. the greater the extent to which you leave the shell intact.
Cut an inspection hole in the wall to get an idea of the area you'll need to work with; cut the pipe out; sweat on new piping; install hose bib; patch and repair interior finishes.