"Miley and Liam are done; it's over. She likes to party really hard and can be pretty wild. It became a problem for him," an insider told the newspaper.
"They have broken up before, and are broken up again now. There was drama because she suspected he had a wandering eye. And she recently tweeted a denial that he cheated," a second source said.
"While Miley has insisted they are still together, right now they are very, very much apart."
Hemsworth, 23, and Cyrus, 20, became engaged last May.
The couple started dating when they met on the set of the big-screen romance "The Last Song" in 2009.
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