9:50 AM PT -- The mystery woman is a stage actress named Dylis Croman, who starred with Billy Ray Cyrus in the Broadway production of "Chicago" last year.
Miley Cyrus is turning up the heat on her father ... warning him to "tell the truth" about his relationship with a mystery woman, or she'll blast him for all of the world to see ... via Twitter.
The supposed blackmail first surfaced last night when Miley posted a bizarre tweet to Billy Ray Cyrus -- the tweet contained a picture of a mystery woman along with the caption, "Since you won't reply to my texts I'm giving you an hour to tell the truth or ill tell it for you."
Given the relationship drama between Billy Ray and his wife Tish, we're assuming Miley is suggesting the mystery woman is somehow involved.
Miley has since deleted the post.
FYI -- an "hour" came and went and Miley never followed through on her threat ... unless Billy Ray actually contacted her.
We reached out to Miley's people for comment -- so far, no word back.