For the record, this wasn't out of nowhere. O'Connor took notice of Cyrus in the first place because the former Ms. Montana had told Rolling Stone her "Wrecking Ball" video was strongly influenced by O'Connor's "Nothing Compares 2 U" clip (the close-up shots with the single tear—not the sledgehammer licking scenes).
After getting wind of that, Sinead decided to let Miley (and the world) know that "nothing but harm will come in the long run from allowing yourself to be exploited" in a letter to Miley that didn't pull any punches.
Now, Miley is swinging her wrecking ball toward the Irish singer by linking her to the most famous meltdown of 2013. Cyrus tweeted, "Before Amanda Bynes, there was…" and then inserted a picture of one of O'Connor's infamous Twitter rants. Which—if you know O'Connor's history—is a major insult. She's battled depression and bipolar disorder for years, a fight that has occasionally leaked into the public eye via online rants.
While Cyrus' tweet works as an effective zing in a sitcom environment, she's missing the point by dismissing someone's opinion simply because they also struggle with mental illness. Plus, O'Connor's letter isn't so much an attack as it is free (albeit unsolicited) advice: She also praises Cyrus as displaying "obvious talent" and argues that sledgehammer-licking antics will only "obscure your talent by allowing yourself to be pimped."
So while Miley might understandably want to bite back, she's better off steering clear of mocking someone's mental illness. Our advice: Take a page from O'Connor's SNL playbook and rip a pic of the Irish singer in half when she hosts this weekend. At least that insult also works as an homage.