Great question!
There is a book-length answer by Melissa Mohr: Holy Shit: A Brief History of Swearing. Helpfully enough, the book starts out with a section on the curse words of the Roman Empire. I don’t have my copy on hand, but I can give you the gist and I suggest picking one up if you’re interested.
Mohr’s basic thesis is reflected in the title of her book: through time and across societies, curse words tend to fall into two distinct categories: the holy of religious words (Jesus Christ, hell, damn, goddamnit) and the shit of anatomical, sexual, and scatalogical words (fuck, piss, asshole, cunt, shit). The relative severity of the two groups depends on the specific culture we’re talking about.
Romans, like most societies, loved to swear. Their “holy” swears resembled ours quite closely - invocations of various gods and theological concepts. What I personally find more interesting are their “shit” swears, and what they reveal about Roman body politics.
At first blush, Roman anatomical swearing was also pretty similar to our own. Their dirty lexicon included close parallels (on both meaning and usage) to shit, piss, asshole, cunt, and dick. What’s interesting are the Roman swears that don’t have direct parallels in modern English and vice versa.
One Roman swear that doesn’t appear in English is a vulgar term for clitoris. On some level, it seems like this should be an obvious go-to: we have swears for nearly every other piece of sexual anatomy, so why not that one? But get into a bar fight and insult your opponent with “You know what, you’re a fucking clit!” and you’ll get nothing more than confused looks. Why?
In contrast to modern American society, much of Roman anxiety about homosexuality had to do with lesbian intercourse. There was a widespread belief that certain lesbians developed massively enlarged clitorises which could be used for penetrative sex with other women, and this (likely fictional) act was seen as the sine qua non of perversion. Thus, in Roman society, the clitoris was seen as a dangerous, penetrative object in a way that it is not in contemporary western society.
We see a similar theme in Roman swears about male sexuality. In America, if you really want to insult a man, you call him a homosexual (f*ggot, queer, homo, etc) - until a few years ago anyway and still in many parts of the country. But those swears didn’t really work in a society where sex between men and boys was normalized. Rather, the Roman preoccupation was with sexual role: the dominant/penetrative/masculine versus the submissive/penetrated/feminine. The severest insults for men would be the ones that suggested he enjoyed or readily submitted to the penetrated role - basically, in modern English, calling him a bottom. We have one record of a note sent between two guests after a dinner where they were treated horribly rudely by their host, wherein one guest complains to the other at length about their treatment and closes with something to the effect of “I would rape him in the mouth, but he’d just enjoy it.” Harsh. That was about as insulting as you could get.
So, in summary, stubbing your toe on your way home from a day at the gladiator fights would produce mostly the same swears as closing your hand in the car door at Whole Foods - apart from being in Latin of course. The points where Roman swearing diverge sharply from what we are used to provide interesting insights into Roman anxieties and taboos.