How to remove copper pipe that is inside an exterior wall?
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.