In the following pictures featuring our own very pregnantly round, Jairica Stepford, we can see how to properly cut the ends off.
Rather than taking a knife and uniformly cutting the ends, she holds both sides and bends the stalk until it snaps in half naturally. This natural break point is typically the weak spot between the healthy moist portion and the dried out end that you would want to discard. After asparagus has been harvested it begins to loose moisture out of the end, and it is important to realize that no piece is the same. That is why it is wasteful to use a knife and cut all of them equally.