Donald Trump's star on the Hollywood Blvd Walk of Fame is completely destroyed after someone took a pickax to it ... and LAPD is on the case.

Law enforcement sources tell us Trump's star was smashed apart early Wednesday morning. We're told the vandal posed as a construction worker to fool anyone walking past while they did the damage. Cops took a vandalism report, but haven't made any arrests.

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According to Deadline Hollywood ... someone who said his name is Jamie Otis took credit for the destruction. He said he intended to auction off the removed star to raise money for the legal defense of Trump accusers.