Kyutoryu is an addition to Zoro's main Santoryu style of swordmanship that uses, as the name suggests, "nine swords". Thus, Kyutoryu effectively triples Zoro's potential power.
Kyutoryu is shown to be an extension of Zoro's spirit and part-illusion: using the style creates a vision of Zoro acquiring two additional heads for three total, as well as four more arms for a total of six, all wielding copies of his swords for a total of nine blades, making Zoro resemble the mythological "asura".
Following the two-year timeskip, Zoro might have incorporated Haoshoku Haki into his Kyutoryu as stated by Kaido (although, he was unaware of this fact); it is unclear if Zoro's pre-timeskip usage of Kyutoryu involved Haoshoku or, if at all, Busoshoku Haki.
Kyutoryu was developed by Zoro sometime prior to—and first seen used during—his fight against Kaku, overpowering the latter's most powerful Rankyaku before defeating the CP9 member. In-canon, Zoro has only used Kyutoryu thrice so far: two times pre-timeskip, with one additional instance of use during the events of Movie 10, and against Kaido after the timeskip.
Kiki Kyutoryu: Ashura (鬼気 九刀流 阿修羅,Kiki Kyūtōryū: Ashura?, literally meaning "Ghastly Nine Sword/Blade Style: Asura"): The basis for Kyutoryu. Zoro, with his Wado Ichimonji in his mouth and his other two blades held out in front of him, creates an illusion born of his "spirit" (気迫,kihaku?), according to Kaku. To onlookers, it appears as if Zoro gains an additional pair of heads and four more arms, all wielding duplicates of his swords—each appearing twice more, for nine swords total. At the same time, an indistinct, six-armed, asura-like silhouette forms behind Zoro, the same entity he comes to resemble, described by Kaku as a "three-faced, six-armed demon god" (三面六手の鬼神,sanmen-rokushu no kishin?). The anime further adds to the first-seen activation of Asura: Zoro, angered by Kaku, had a dark aura begin surrounding him, expanding several meters around where he stood and causing a swirling gust to form. "Ashura" (阿修羅,"Ashura"?) is the Japanese term for "asura", a class of demons/demigods from Hindu and Buddhist mythology. In the Viz manga, the technique is called Demon Aura Nine Sword Style: Asura and, in the FUNimation sub and dub, the name is Demon Aura Nine-Sword Style Asura.
Before the Timeskip
Ashura: Ichibugin (阿修羅 弌霧銀,Ashura: Ichibugin?, literally meaning "Asura: One Mist Silver"): The first derivate Kyutoryu attack that is seen, used by Zoro to finish off Kaku. Zoro, holding his swords so that the blades are pointing toward the enemy, leaps toward them at great speeds, powerfully slashing them with all "nine" of his swords at once and ending up behind the enemy's back, holding his blades in a manner that makes them look fanned out. The attack was strong enough to disperse Kaku's Rankyaku "Amane Dachi"—his strongest attack—turning the massive slash wave into "mist" (a nod to the attack's name) before slicing up Kaku in his human-giraffe form so thoroughly as to defeat him. The technique's name is a pun on "ichibugin" (一分銀,"ichibugin"?), meaning "a silver quarter ryō". In the Viz Manga and FUNimation dub, the attack is called Asura: Silver Mist, and in the English dub of the game One Piece: Unlimited Cruise it is called Asura Ichibugin. In the Wii video games, the "Unlimited" series, and Gigant Battle, this move does not see Zoro charging against the opponent, instead producing a longer-ranged, expanding shockwave.
Ashura: Makyusen (阿修羅 魔九閃,Ashura: Makyūsen?, literally meaning "Asura: Demonic Nine Flashes"): An attack similar to Ichibugin, where Zoro in his "Asura" state approaches the enemy to consequently slice them up with his nine swords, before ending up in a stance that has the blades resemble a wheel shape. The attack was first seen in use against the Pacifista PX-4, breaking through its harder-than-steel armoring to draw blood from the cyborg. In the anime, the game Unlimited Cruise, and the Pirate Warriors games, the move has Zoro perform a rotatory motion that is not observed in the manga. In the Viz manga, the technique is called Demon Nine Flashes while in the in the FUNimation sub of the anime, it is called Asura's Nine Lightning Strikes.
After the Timeskip
Ashura Bakkei: Moja no Tawamure (阿修羅抜剣亡者戯,Ashura Bakkei: Mōja no Tawamure?, literally meaning "Asura Sword-Drawing: Jest of the Dead"): A powerful Kyutoryu technique that may involve Haoshoku Haki, speculated by Kaido. Zoro holds Enma out before him, horizontally in his right hand, his other swords held in his left hand and mouth as usual, entering the "Asura" state, with the silhouette behind him clasping two of its six hands. Haki begins emanating from Zoro as he imbues his blades with it, turning them black. He then, readying his blades, moves past his opponent in a flash, cutting them with incredible force. The attack was first used on Kaido, with Zoro putting all his remaining strength into the slash. It proved strong enough to significantly injure the Emperor, giving him a large, bloody gash across his front torso; Kaido, while remaining on his feet, acknowledged that the blow would leave a scar (which would make it the second technique ever to give Kaido a permanant scar). The attack's name references Jigoku-bakkei Mōja no Tawamure (地獄八景亡者戯,Jigoku-bakkei Mōja no Tawamure? "The Eight Scenes of Hell, Jest of the Dead"), a Kamigata Rakugo play from the Edo period. Instead of the usual "hakkei" (八景,"hakkei"?), said kanji are read "bakkei", with the name of this attack using "Bakkei" (抜剣,"Bakkei"? literally meaning "Drawing One's Sword", though correctly read "Bakken") to play on the pronunciation. Unlike previous Kyutoryu uses, the kanji for "Asura" are accompanied by hiragana, not katakana. The Viz Manga calls the attack Asura: Blades Drawn Dead Man's Game.
Ashura: Ugui (阿修羅穿威,Ashura: Ugui?, literally meaning "Asura: Piercing Might"): An attack only seen in Zoro's during his fight against Indigo in One Piece Film: Strong World. The move quite resembles Zoro's other Kyutoryu attacks, the main difference being that, as Zoro rushes past his enemy, violently slicing them with his illusionary nine blades, said enemy is blown high into the air from the impact. Using this technique, Zoro defeated Indigo in a single blow, despite the scientist having sustained no prior injury in their fight. The technique's name likely comes from "ugui" (石斑魚,"ugui"?), the Japanese name of the big-scaled redfin, a species of fish. The movie's Funimation dub calls the attack Asura: Piercing Drill.
The "asuras" (Sanskrit: असुर) are a class of powerful, power-hungry demigods—often portrayed as demonic with three heads and six arms—that appear in Indian religions. They are featured in many Buddhist and Hindu cosmological theories, and in both Buddhism and Hinduism are prominently described as battling the more benevolent, heavenly "devas" or "suras" (gods), being considered the "enemy of the gods" in Vedic and post-Vedic literature. More specifically in Buddhism, asuras ("antigods", "demigods", or "titans") constitute the third of the six Saṃsāric realms of rebirth and existence that reincarnation into occurs based on karma gathered in current or past lives. Into the realm of asuras, people are reborn due to actions based on jealousy, struggle, combat, or rationalization in a previous life.
Thus, Zoro's Kyutoryu follows the theme of his other sword techniques that often incorporate Buddhist terminology/imagery, as well as "demonic" motifs.
Upon first seeing the illusion of Zoro with three heads and six arms, with the figure behind him, Kaku described what he saw as a "demon god" (鬼神,kishin?). This term, which most literally translates as "demon/oni god", is usually used to refer to "fierce" or "wrathful deities" in Buddhist myth (wrathful "aspects" of enlightened buddhas, bodhisattvas, or devas), but is also applicable to more "demonic" beings with superhuman power/ability, such as asuras or rakshasas, as well as "fierce" Shinto gods.
The concept of an attack of nine simultaneous slashes the Kyutoryu uses is similar to the Rurouni Kenshin's protagonist Kenshin Himura's technique Kuzu Ryusen. Curiously Eiichiro Oda worked as an assistant for Nobuhiro Watsuki, Rurouni Kenshin's author.
Kyutoryu is the style Zoro didn't use for the longest in the manga: in fact between its first and last use, there is almost 15 years in real life.
↑ 1.01.11.21.3One Piece Manga and Anime — Vol. 43Chapter 417 (p. 16-17) and Episode 300, As Zoro prepares his Kyutoryu to use against Kaku, the latter recognizes the vision he sees as a product of his spirit.
↑ 2.02.12.2One Piece Manga —
Chapter 1010 (p. 8-9), Zoro uses Asura: Bakkei Moja no Tawamure against Kaido.