If you don't mind the muffler obtaining a blackish tan, use a caustic soda solution (NaOH), and some heat. This will dissolve even carbon deposits. The black surface film can later be etched away with acid based metal cleaners. For mufflers this is ok.
Or:
you heat the muffler submerged in synthetic oil, or anti-freeze fluid (The "crock method"), and then brush with a brass wire brush and tooth paste. (steel and aluminum don't like each other)