Skinning or flaying was the act of removing the skin from an animal.
According to legend, Kahless the Unforgettable skinned the Serpent of Xol with the Sword of Kahless. (DS9: "The Sword of Kahless")
In 2266, James T. Kirk promised Montgomery Scott that they would see the jackass known as "Leo Walsh" skinned. (TOS: "Mudd's Women")
The phrase "more than one way to skin a cat" meant that there were multiple methods to achieve an objective, beyond the most obvious or recent attempt. According to an account that was anything but canon, when the captain of the USS Enterprise used this figure of speech, M'Ress was quite angry, believing that Humans actually skinned cats. The captain admitted he didn't know the origin of the expression, immediately assuming it was the old pioneers, but he tried to reassure her that he never skinned cats, nor would he. (VST: "Skin a Cat")