Scissor Blades

The Scissor Blades, known as the Rending Scissors when combined, are a giant pair of scissors developed by Isshin Matoi specifically for cutting Life Fibers, that were divided into two weapons shortly before his death. They are made from hardened Life Fibers, making them the only weapons (beside Satsuki Kiryūin's Bakuzan) that are capable of cutting any Goku Uniform or Kamui, except for Ragyō Kiryūin's Shinra-Kōketsu, which is also made of hardened Life Fibers. It is unknown what happened to the Scissor Blades after Episode 24, as Ryūko is not shown bringing them back to Earth with her.

Red Scissor Blade
Ryūko Matoi owns the red half of the Scissor Blade. The crescent-shaped hilt can extend into a longer two handed sword, known as Decapitation Mode. Ryuko's signature finishing move is Fiber Lost, a long-range forward thrust that completely destroys a Goku Uniform, allowing her to absorb its Life Fibers.

The red Scissor Blade also displays the ability to change its size, going from a weapon that is nearly as tall as Ryūko to a trinket barely any larger than a normal set of scissors. Ryūko usually keeps the blade in its smaller form when not in a combat situation, but also owns a metal guitar case that can carry her weapon around.

Purple Scissor Blade
The second half of the Scissor Blade spends most of the series in Nui Harime's possession. Unlike Ryūko's half, it has a circular handle and a slightly more angular tip, making it slightly shorter than its counterpart. It can reconfigure into a stronger form that adds a curved scythe blade to both ends. It was eventually recovered by Ryūko in Episode 22 during the fight against Nui, officially completing the former's weapon set.

This half of the Scissor Blade appears capable of changing color. It is shown to be red during Isshin's murder, purple when in Nui's possession, and red once again when Ryūko retrieves it.

Rending Scissors
When the Scissor Blades are used together, they are able to sever Life Fibers as well as prevent their regeneration, as shown by Nui's loss of her eye and arms (done by Isshin/Sōichirō and Ryūko respectively). Even though the Rending Scissors need to be used together to activate this effect, they do not need to be combined together to use this effect, meaning that it can have the same effect even when it is divided into two halves. In Episode 23, both the Scissor Blades go into "Decapitation Mode", implying that they have all the abilities of the separate blades (including a dual scythe form and the ability to shrink to the size of normal scissors).

In Episode 24, Ryuko finally reforms the original Rending Scissors after transforming Senketsu into Senketsu Kisaragi. The Scissor Blades were bolted together by a screw that appeared from thin air. In this form, they retain their ability to extend their blades, forming a pincer-like weapon called "Dual Decapitation Mode."

Trivia

 * The boss character Mighty No. 7, from the upcoming video game Mighty No. 9, wields two halves of a giant red scissor that bear a striking resemblance to the one wielded by Ryūko, indicating a possible reference to Kill la Kill.