I touched on this very briefly in my answer on What are the Origins (or truth) of the Donkey Show Myth. Apuleius in The Golden Ass has a female poisoner sentenced to be raped by a donkey, this (fictional) punishment appears to have inspired quite a bit of thinking along those lines, and some confusion with historical reality. Of the primary sources of her life, only one discusses her execution:

In the case, however, of Helius, Narcissus, Patrobius, Lucusta, the sorceress, and others of the scum that had come to the surface in Nero's day, he ordered them to be led in chains throughout the whole city and then to be executed.

• Cassius Deo, 63.3

"Sorceress" in this case should be read as "poisoner," as the two were sometimes synonymous. Her case, however, appears to have been confused with some fictional embellishments by much later authors.

Carpophorus used up several women before he got the animals properly trained -- with a bull or a giraffe the woman usually didn't survive the ordeal -- but he was always able to get more broken-down old bags from the provinces who didn't fully realize what their job involved until too late.

[...] A woman who had poisoned five people in order to get their property was sentenced to be thrown to the wild beasts in the arena but first, as an additional punishment and disgrace, she was to be raped by a jackass.

• Daniel P. Mannix, Those About To Die (1958)

The first section is Mannix own invention, a lurid idea of how bestiality shows might have been staged in or under the Coliseum in Rome. The second section is plainly borrowed from The Golden Ass. It is probable that later writers, equally shoddy with their historical research, combined the two ideas when it came to Locusta. The earliest account I know of where the claim is made is Michael Newton's Bad Girls Do It! An Encyclopedia of Female Murderers (1993), who wrote:

As described by Apuleius a century later, Locusta's execution was timed to coincide with one of the frequent Roman festivals - probably the Agonalia (for Janus), held on January 9. On orders from Galba, Locusta was publicly raped by a specially trained giraffe, after which she was torn apart by wild animals.

Here, Newton is making two mistakes: assuming that Apuleius' fictional account is real, and using "giraffe" instead of "jackass" or donkey. This appears to be the major source of all subsequent urban myths regarding Locusta and the giraffe, although it's always difficult to say that with 100% certainty.

I can't speak to this particular claim, but execution spectacles with themes taken from mythology or popular dramas and sometimes involving trained or wild animals were definitely practiced in the Roman arena in the first century AD. The historian Kathleen Coleman calls these "fatal charades". (https://www.jstor.org/stable/300280?seq=1) These were horrifying by modern standards but some later authors have also invented similar atrocities; there are all kinds of stories for which no contemporary record can be found.

That said, the poet Martial records a spectacle similar to the one you have described in his De Spectaculis, which is a celebration of games held under Domitian around 80AD when the Flavian Amphitheatre was opened. These games included something along the lines of a reenactment of the myth of Pasiphae and the Bull (mating to create the Minotaur). Martial was in the audience and writes:

That Pasiphae coupled with the Cretan bull—believe it! We’ve seen it: the fable we used to have to take on faith. You shouldn’t be surprised, Caesar, at such an old tale retold. Whatever myth sings, the arena presents you with.

• Martial, De Spectabilis V (Art Beck, Mea Roma, 2018 translation)

This is usually interpreted as an execution by bestiality. It's possible that there was some kind of stagecraft involved but Martial wants his reader to believe that it really happened.