A common way of making monsters or fantastic creatures is to simply take existing animals and combine their parts. For instance, the Classical Chimera (lion head, goat body, snake tail) or the Minotaur (bull head, human body). Also common is to simply take an existing animal and vary it a simple way — Pegasus is a horse but with wings, hippocampi have the heads and front bodies of horses but the tails of fish, etc.
Another common variant is to make a Punny Name of a real life animal named after a different animal: for example, a "catfish" that is literally half cat, half fish. For those cases, see Pun-Based Creature.
Compare Fusion Dance and Two Beings, One Body, which is when two characters are combined. Shapeshifter Mashup usually results in this. Mix-and-Match Critters may be the result of Hot Skitty-on-Wailord Action. If both creatures are already mythological/magical/whatever and get mixed, they have a newborn Hybrid Monster and if mundane they can end up with a Patchwork Kid. Application of the principle to humans may count as Bio-Augmentation, see also Mix-and-Match Man. Mons often have aspects of different animals. Puzzling Platypus may count as a Real Life example of this trope.
Mix-and-Match Critters has been suggested to play 4 roles. Click below to see other actors suggested for each role, and vote for who you think would play the role best.