Born in Birmingham, Joseph Moore was apprenticed at a young age to diesinker Thomas Halliday. He also trained under Samuel Lines, another diesinker and engraver. After completing his apprenticeship he began his own business as a buttonmaker, winning a prize at the 1851 London Exhibition for his work. While engaged in his apprenticeship and working as a buttonmaker, he studied in his own time to gain the skills of a medallist.
In 1844, it was suggested to Moore that he might make a coin which would be an improvement on the heavy and cumbersome penny-piece which was then in currency. He designed a model penny - absolutely his own idea - of about the size of a farthing, inside the raised rim of which was a small piece of silver which brought its value up to the proper standard. The rim was ingeniously devised with the object of making the penny distinguish- able from other coins of a similar size in the pocket merely by feeling it. There was an enormous demand for these tokens; so great, indeed, that Wyon, the coin die-sinker to the Mint, when he came to consult Moore about his system of making dies so that they would not break, good-humouredly explained that they had met with such favour with the public that he had been compelled to advertise the fact that they were the result of private enterprise and not a Government issue.
Moore created some of the dies used by Heaton and Sons to produce coins and tokens. He is also credited as the designer of the penny and halfpenny tokens issued by Professor Holloway in 1857 and 1858.
Some of his designs are: