Yes, what if David Lynch directed Dirty Dancing? Re-cut trailers are a form of mashup art, short clips featuring rearranged footage and a different spin on the original movie.
Watch Stephen King's IT transform into a feelgood family adventure, Mary Poppins getting scary, or Brokeback Future, aka the true story of Doc Murphy and Marty McFly.
I could not find a repository or some sort of index for the recut scene, but googling "recut trailer" should give you a good starting point.