The production of coins within Republican Rome was under the direction of the tresviri monetales. They are referred to by Pomponius (Digest) as the triumviri monetales aeris argenti auri flatores which is basically 'the three men for casting and striking of bronze, silver, and gold.' The position of monetales was an introductory position into Roman public life. When such position was introduced is unknown, some scholars suggest a date of 290-289 BC based upon the introduction of other similar offices, some scholars suggest 269 BC given the date that a Roman mint began to produce silver coins, and some just believe that we do not know but establish the foundation to the 3rd century BC.

The mint of Rome was a building on the Capitoline Hill located next to the temple of Juno Moneta. The triumviri monetales would supervise the production of said coins including the type (design) included on the coin, which would then be struck by the mint workers (monetarii). It was under there supervision then that it would be expected to understand how many coins were to be produced. The method of striking coin was simple. The designs for the obverse and reverse of the coins would be engraved into metal known as dies. One die would be placed in an anvil and the other in a metal bar, the soon to be coin was placed inbetween and a hammer was then used to make an imprint.

The production of coins was pretty standard between 218 BC - 140 BC. Bronze coinage (aes grave) had standard designs for the most part made up of six types: the As (Head of Janus/Prow); the Semis (Head of Saturn/Prow); the Triens (Head of Minerva/Prow); the Quadrans (Head of Hercules/Prow); the Sextans (Head of Mercury/Prow); and the Uncias (Head of Roma/Prow). Likewise, the silver coins (denarii) for the most part included designs related to the state such as Roma, Hercules, the Wolf and Romulus and Remus, the Dioscuri and so on.

It was in the 130s BC in which we begin to see the iconography of coins beginning to change annually with the focus being political propaganda. The reasoning behind this change is suggested as being because of an increase in political competition during the period (I myself believe it had been ongoing for decades prior). Another influence may have been the lex Gabinia Tabellaria in 139 BC which introduced secret ballloting - the use of coins as propaganda then became more important. From then on the position of monetale became important as one could issue coins outlining the achievements of their families and alike (this could have also been simply a way of remembering their family members - something which was important in Republican Rome).

 

In terms of stealing within the Roman Republic, I am not aware of any cases of the mint itself being robbed. The mint was provided with the metal they striked by either the state or individual citizens so they would know how much metal they provided and therefore how much coin they should receive. However, there was issues with forgery.

According to Pliny (Natural History. 33.13.46), it was Livius Drusus (tribune of the plebs) in 91 BC who produced a silver coin alloyed with one-eight of copper. According to Cicero, the issue became that bad by 85 BC that the tribunes of the people and praetors took action to standardise the value of currency, because (On Duties. 3.20.80):

...or at that time the value of money was so fluctuating that no one could tell how much he was worth.

Sulla introduced a law in 82 BC as dictator known as the lex Cornelia de Falsis which considered forgery as an act of falsum (fraud) and a crimen publicum (crime against the public) and would result in severe punishment.

If you are interested further in books then really the best place to start is M. Crawford. More recently published books will no doubt reference back to Crawford.

Crawford, M. (1974). Roman Republican Coinage, London.

Crawford, M. (1985). Coinage and Money under the Roman Republican: Italy and the Mediterranean Economy. London.

At least in the Late Republic, but I think also earlier and definitely later, the Romans had "governmental" mints. On the Roman Imperial coinage (RIC), the mark SC, Senatus Consulto, showed that the coin was created in one of these mints. Before that, usually the mint masters (tresviri monetales) would put their name on the coins. This way, one could see which coin was made by decree of the senate and which one wasn't.

The coins would be produced in batches: there would be a mold with an reverse and a die with an obverse, which would then both be imprinted in the metal(either gold, silver or bronze).

I'm not sure how they made sure that nobody stole coins while producing, but the tresviri monetales come from senatorial families, so they were of high(er) status. The senate would also know these people personally, so I don't think stealing coins from these mints was profitable.

Maybe these sources are interesting for you:

Hamilton, C. D. (1969, January). The tresviri monetales and the republican cursus honorum. In Transactions and Proceedings of the American Philological Association (Vol. 100, pp. 181-199). Johns Hopkins University Press, American Philological Association.

Wallace-Hadrill, A. (1986). Image and Authority in the Coinage of Augustus. The Journal of Roman Studies, 76, 66-87.

Metcalf, W.E., “Roman Imperial Numismatics”, in: D. Potter (ed.), A Companion to the Roman Empire (London 2006), pp. 35-44.

Hope this helps!

Actually during the reign of Aurellian there was a rebellion of mint workers. It's not very well documented, unfortunately, but what we do know is that the person in charge of the Roman mint, a gent by the name of Felicissimus, allowed the the silver content of the coins to slip below official levels with the extra silver being pocketed by the workers. Felicissimus was executed for allowing this to occur, and his workers rebelled en masse. The Roman mint was temporarily shut down, which happened to be one of the steps in making the city of Rome less important to Romans. In about a decade the official capital would be Milan (which happened to have its own mint working in overtime while Rome's was shut down).