In rewatching (for about the 8th time) a few episodes of Time Team (in this case, Season 12, episode 10), Guy de la Bedoyere mentions that Romans tended to donate/sacrifice broken jewellery and cheap/bad/damaged/forged coinage to temples and holy sites.
My understanding is that pre-Roman Iron Age and Bronze Age cultures across Europe would often make specific, "ritual quality" items, purposely break them, then lay them in sacred places (presumably to make it unsuitable for the living, and thus useful for the dead/gods?).
But I dont know if Romans purposely broke their items for the same reasons before offering them, of if the plethora of broken and poor quality offerings was more of a result of frugal, potentially cheeky Romans who had broken items, or were given bad or low value coins, and decided they "would do" for the Gods. (I think I remember something about food offerings for the gods being largely the inedible or unpleasant parts...)
Can anyone comment on that?
The coins were mutilated (the technical term) deliberately, but the motivation for this behavior is not entirely clear. It is not a very common topic in academic circles, but there is at least one very focused study of ritual coin mutilation: G. Aubin and J. Meissonnier, "L'usage de la monnaie sur les sites de sanctuaires de l'Ouest de la Gaule et de la Bourgogne," Archeologie Aujord'Hui - Sanctuaires de tradition indigene en Gentle Romaine. Actes du Colloque d'Argentomagus (Paris, 1992), 143-5. For your question: a scenario of a temple patron cheekily using a useless coin instead of a "good" coin to "one-up" the god is not really a realistic scenario of ancient religion, be it Celtic, Roman, or otherwise. A votive offering with was the dedicator's physical contract with the god, and offering up something both you and the god would consider substandard or flawed is anathema to that behavior.
There were many varieties of intentional damage: cutting into the face(s) of the coin, striping or denting its edges, bending it, folding it, etc. There is not one winning theory as to why: some think that the coins were slashed, perhaps by religious authorities, to test that they were authentic and not plated. I personally do not place much weight on this, as many of the coins are slashed multiple times, and then also bent. I think the best explanation is that the coins were "killed" in order to ensure their status as votive offerings--in essence, to remove them from secular circulation. Upon their dedication, the coins become ritual objects, physical markers, and no longer currency. This makes perfect sense for those who have studied ritual behaviors going back into the Iron Age, as you have said.
The practice of "killing" votive objects is nothing new in Early Iron Age practice. We find it all over the Iron Age Indo-European world. So-called "Warrior Graves" from France to Spain to Italy to Greece very frequently feature "killed" weapons, bronze or iron, which have been bent or otherwise mutilated. They are ritually and symbolically destroyed to mark them out as sacrificial offerings commensurate with the prestige of the deceased. In a similar way, the pottery associated with the funeral feast was "killed" after its use, and the sherds deposited on the pyre along with the body. Sometimes this behavior even extended to living things, like the four horses ritually slain for the "Big Man" at Lefkandi, or the human female who was (presumably) killed at the funeral of the occupant of the royal tomb at Vergina. In all these cases, the mutilation of the object is not functional--it isn't as if someone would dig up the grave and then employ the sword as a sword again. Similarly, many mutilated coins wind up in springs or wells, and had no possibility of being retrieved and spent as money again. The mutilation is deliberate and ritualistic in nature.
Side note: Even into the Late Iron Age and beyond, it was common in Celtic areas, especially the Alps, northern Gaul, and some sites in Britain, to ritually destroy objects by throwing them in the water. Many Alpine lakes have yielded hoards of Celtic dedicatory offerings. This practice seems to be why many mutilated coins (and other objects) from the Roman period wind up in water, like at Bath or "Coventina's Well" in the north of England.