Can monsters use the mystic slide
Yes, monsters can use any special room as they want.*

From the rulebook:


  Like traitors, monsters can ignore all nondamaging room features. They can use the Coal Chute, Collapsed Room, Gallery, Mystic Elevator, and stairs tiles, along with many of the special movement options described on cards (such as
  the Secret Stairs), unless those cards say that only explorers can use them. They ignore the effect of the Furnace Room and the Crypt.


And the official FAQ:


  Can monsters use the Secret Stairs, Secret Passage, Revolving Wall, and Mystic Slide to
  move around?
  
  
    Yes. It's their house, after all. (Besides, it's possible for these to create areas of the house that can't be reached any other way, and some scenarios won't work if monsters can't reach all rooms.) Ignore the section of the rules that states, "unless those cards state that only explorers can use them." Also, a monster wouldn't need to roll to use the revolving wall.
  


*Note that this does not include stat-gaining rooms such as Chapel, Gymnasium, Larder, and Library. From the FAQ:


  Chapel, Gymnasium, Larder, Library -- Can monsters use these rooms?
  
  
    No. Unless a monster is actually a transformed traitor (a werewolf, for instance), its attributes usually do not change.