Phrase Finder says the origin of the term is obscure, but does offer "... The similarity between "fired" and "discharged" may suggest a connection with firearms. I could find no real origin in any of my reference books, other than suggesting the analogy with firing a gun. However, one day, I was sent the following which appeared in the Clevedon, Somerset, Civic Society Newsletter for Summer 1996:
"We discovered recently that the word 'fired', meaning discharged from a job originated on Mendip. It comes from Item 6 of the Laws of Mendip Miners.
"If any man... do pick or steale any lead or ore to the value of xiiid (=13 pence), the Lord or his Officer may arrest all his lead and Oare House or hearthes with his Grooves and Workes and keep them in forfeit... and shall take the person that hath soe affeended and bring him where his house or worke and all his tooles and instruments are... and put him into his house or worke and set fire in all together about him and banish him..." Fired indeed!"