Here's a little trick that works really well for those types of labels. Have you watched professional wrappers at Christmas time curling ribbon with a pair of scissors? It works for removing the backing from the labels as well. Hold the backing of the label against the side of a pair of scissors / knife / even a key with some sharper points on it, and drag it across the edge. This will make the ends separate a little bit, allowing you to take hold and easily separate the pieces.
Check out this site that shows it being done with scissors if you've never seen it
Make sure it's the backing side being scraped across the scissors, not the printed side.