Look at the nail closely and you'll see it really has two parts. The long large part that grows from the digit, and the almost needle-like part at the end. Just cut the end part. The long large part will bleed if you cut it.

Hope that clears things up. That's why everyone is suggesting cutting in the sun, you can really see the difference, and what needs cutting.

I cut my boy's nails at first but since I added one large piece of tile as a roof to a hide, he crawls around that enough that it wears them down naturally. I still have to occasionally trim one or two, but not all of them like i used to.