"The fox has a mouse."
Translation:여우가 쥐를 가지고 있어요.
It means to possess. Since it is currently in possession you use the continuous conjugation.
How would the meaning change if it was in the present? (as in 가져요 (I believe XD))
ahh, I wrote 여우는 쥐가 가지고 있어요 instead of 여우가 쥐를 가지고 있어요. Thought 있어요 couldn't have an object, but obviously 가지고 있어요 is the whole verb.