The saying comes from the Middle East, where as punishment, liars had their tongues ripped out and fed to the king’s cats.
Fear of a whipping with a cat-o’-nine-tails, or “cat” for short, could paralyze a victim into silence.
The expression comes from the Middle Ages when witches were greatly feared and often put to death. It was believed that if you saw a witch, her cat would somehow “steal” or control your tongue so you couldn’t report the sighting.
This one comes from Evan Morris, the Word Detective: “There’s no particular logic to ‘cat got your tongue,’ except that cats have served as the object of human myth and metaphor for thousands of years.”
Source: Ask Yahoo