Scissor Blades

The Scissor Blades (片太刀鋏) are special weapons developed specifically to cut Life Fibers. They were created by Isshin Matoi as one single pair of scissors, the Rending Scissors (断ち斬りバサミ), and were divided in the moment of his murder.

Red Scissor Blade
Ryūko Matoi owns the red half of the Scissor Blade. It can expand into a longer sword (known as Decapitation Mode) or collapse into a normal size scissor half.

Purple Scissor Blade
Nui Harime formerly owned the purple half of the Scissor Blade. Unlike Ryūko's half, it has a circular handle. It can change into a dual scythe mode with a scythe at either end.

This half of the Scissor Blade seems to have changed color at some point, since it is shown to be red during Isshin's murder. It then turned red once again when recovered by Ryūko.

It was eventually recovered by Ryūko in order to fight against Nui, officially completing the former's weapon set.

Wielded Together
When the scissor blades 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 respectivly).

Trivia

 * The boss character Mighty No. 7, from the upcoming video game Mighty No. 9, wields two halves of a giant red scissor thar bear a striking resemblance to the one wielded by Ryūko, indicating a possible reference to the Kill la Kill series.
 * It is unknown why the blades didn't changed color when both were in Nui's possession, and did changed when Ryūko retrieved it without having to modify the color.