Nicki Minaj curses out Mariah Carey on the set of US Idol

Nicki Minaj derailed the "American Idol" auditions in Charlotte, North Carolina Tuesday, after swearing at Mariah Carey and threatening, "I'm gonna knock you out" ... but Mariah FIRED RIGHT BACK with insults of her own.

In the footage, obtained by TMZ, Nicki is clearly furious ... shouting, "I told them I'm not f*ckin' putting up with her f**kin' highness over there."

Mariah can be heard saying, "“Oh why, WHYYYY .do I have a three year old sitting around me?”

Carey continues, "I can’t see my kids, because you decided to act like a little crazy bitch and go all around the stage.”

Sources say Nicki later threatened to "knock out" Mariah ... but she said it before the video starts.