Can I peel a mandarin orange like the commercial canners do?
In theory, yes you can. Whether you want to is a completely different question.



The segments are "peeled" by soaking them in hydrochlorid acid. Which sounds worse than it is, because the concentration is somewhere between 1% and 0.3% (sources vary). (1)
Once the outer skin is dissolved, the acid is neutralized by dumping them in a lye bath (sodium hydroxide). 
Finally a good long soak in plain water to get rid of whatever might still cling to the fruit and then it's off to the canner.

Other sources claim that the segments are simply peeled by soaking in a lye bath and then rinsed. (2)
A third source quotes a Dutch magazine and claims it's lye first and hydrochloric acid later. (3)


Note that hydrochloric acid and sodium hydroxide form NaCl and H2O or, plainly put, salt water if the ratios are correct. So apparently the whole process is quite harmless for us consumers.



Sources:
(1)  German Wikipedia; Die Zeit (both in German)
(2)  English Wikipedia
(3)  nyceyenne (also in German)