While I agree with Renans answer(It can be applied to any mythical creature), here are some ideas for specific mythical creatures.
 
Upper part humans or Semisohominum - from Semisos meaning half and Hominum meaning meaning human. This includes;

 - Centeroids or Semisohominum Equus which includes subspecies; Centaur or [Semisohominum Equus Caballus][1] and Onocentaur or [Semisohominum Equus Asinus][2]
 - Faunus or [Semisohominum Capra][3]            
 - Harpys or [Semisohominum Aves Aegypius][4]
 - Merfolk or [Semisohominum Craniata][5]
 - Naga or [Semisohominum Serpentes][6]

Human-headed or Maximobestia - from Maxime meaning mostlyand Bestia meaning meaning animal.

 - Seamen or [Maximobestia Craniata][7] 
 - Manticore or [Maximobestia Leo][8] 
 - Dogmen or [Maximobestia Canis][9] 
 - Sirpents or [Maximobestia Serpentes][10]

Human with animal head or Maximohominum - from Maxime meaning mostly and Hominum meaning meaning human.

 - Doghead or [Maximohominum Familiarus][11]
 - Minotaur or [Maximohominum taurus][12]
 
Human with some animal parts or Bestiahominum - from Bestia meaning meaning animal and Pars meaning part.


 - Adlet or [Bestiahominum Cruris][13]

 - Angeloids or Bestiahominum Penna which includes subspeices; Angel or
   [Bestiahominum Penna Columbidae][14] and Fairy or [Bestiahominum
   Penna Cimex][15]

 - Oni or [Bestiahominum Cornu][16]

 - Gorgon or [Bestiahominum Anguis][17]


  [1]: https://en.wikipedia.org/wiki/Centaur
  [2]: https://en.wikipedia.org/wiki/Onocentaur
  [3]: https://en.wikipedia.org/wiki/Faun
  [4]: https://en.wikipedia.org/wiki/Harpy
  [5]: https://en.wikipedia.org/wiki/Mermaid
  [6]: https://en.wikipedia.org/wiki/N%C4%81ga
  [7]: https://en.wikipedia.org/wiki/Atargatis
  [8]: https://en.wikipedia.org/wiki/Manticore
  [9]: https://en.wikipedia.org/wiki/Penghou
  [10]: https://en.wikipedia.org/wiki/Zhulong_(mythology)
  [11]: https://en.wikipedia.org/wiki/Cynocephaly
  [12]: https://en.wikipedia.org/wiki/Minotaur
  [13]: https://en.wikipedia.org/wiki/Adlet
  [14]: https://en.wikipedia.org/wiki/Angel
  [15]: https://en.wikipedia.org/wiki/Fairy
  [16]: https://en.wikipedia.org/wiki/Oni
  [17]: https://en.wikipedia.org/wiki/Gorgon