Wow! Surprise answer. catgut is made from guts, but not the guts of cats. Usually, it's from sheep or goats, but it can be cattle, hogs, mules, or donkeys. The original word might be cattle gut, or it might be kit-gut, where "kit" is a word for fiddle, and the gut was used for strings for musical instruments.
To learn more, go to http://en.wikipedia.org/wiki/Cat_gut.