The easiest way to take that book apart would be to cut off the tops of the staples, and then remove a few pages at a time starting with the first page and flipping them over as you remove them to keep them in the same order.
In order to do this, you can try inserting the blade of a small flat screwdriver in between the first page and under the top of the staple. This should give you just enough space to snip each side of the top of the staple using a small pair of end nippers or side cutting pliers. This will just leave the sides of each staple there. As you remove the pages, you will start to expose the staple more and more, and you might eventually be able to pull the rest of it out with a pair of needle-nose pliers.