The song was removed from the album because of a copyright infringement claim. The author of the fictional story of Adrianne Purity Knight, a 20-year-old woman who had been kidnapped and buried alive in a box, filed a suit against Slipknot claiming that the concept of the song was based on his story. 
Corey Taylor, Slipknot's singer and the writer of the song claimed that the lyrics had been written five years before the song was scheduled to be released and that the inspiration for the lyrics had actually come from watching films such as The Collector and Boxing Helena. According to Taylor, only the title of the song was inspired by the Adrianne Purity Knight story. 
Also included in the suit was a short track titled "Frail Limb Nursery", which was a prelude to "Purity" and included samples of a young boy speaking as Adrianne Purity Knight. Rather than risk having the entire album pulled, Slipknot decided to remove the two tracks. They were replaced by the song "Me Inside".
Eventually, Slipknot won the lawsuit and now is able to play Purity live during their performances.
Here's a video of both Frail Limb Nursery and Purity: