According to Hisashi Koinuma, the game will not feature a Canon Story mode and will instead be replaced with an original story mode[3], named as Dream Story, which see a three-way battle between a Pirate Alliance formed by the Straw Hat Pirates and the Whitebeard Pirates, Sakazuki's after timeskip Marine Headquarters and the "Great Pirate Alliance" founded by the ultimate bosses of the game Gekko Moriah and Marshall D. Teach, along with other past enemies.
Prologue
The story starts after the two year timeskip, just after the crew reached the New World. They got surrounded by a Marine fleet led by Monkey D. Garp. He shoots his Ryuusei Meteor against the ship, then the Marine soldiers assault the pirates. After a short battle, which involves all the crew members, Luffy directly attacks an enemy ship with his Gomu Gomu no Rocket and fights Smoker. After this, Luffy comes back to the ship and the Knock Up Stream launches them up to Skypiea.
Difference with the Canon Storyline
The crew does not meet a Marine fleet after their entrance to the New World in the manga. However, they do meet one in the Z's Ambition Arc, though it's led by Momonga.
The crew has never fought against Smoker on a ship, nor against a fleet led by both Smoker and Garp.
Stage 1: Skypiea Arc
Upon their arrival on the White-White Sea, the crew is surprised by a storm released by Enel on his Ark Maxim and the playable character has to reach him[4].
When the character reached the Maxim and defeated Enel, a cutscene starts and shows Enel causing Luffy to fall out of the ark, and the pirate returning and defeating Enel with the Gomu Gomu no Ougon Rifle[4].

Difference with the Canon Storyline
The canon Skypiea Arc is not set after the timeskip and the sky island is not located above the New World.
The Enel story does not start right after the entrance in the White-White Sea, but after the meeting with Conis and Pagaya which is omitted.
Stage 2: Punk Hazard ArcEdit
The arc starts with the crew returning in the New World and landing on the fire side of Punk Hazard. Here they fight against the G-5 Marine soldiers[4] and then Smoker again. In the end, they flee for the laboratory on the ice side of the island[5].
In the structure, they find a lot of strange purple dials and a green one. The purple ones release a dark fog which makes almost all the Straw Hat Pirates evil. Luffy and Nami, the only ones who were unaffected, flee out[5].

Later Luffy and Nami talk with Smoker[5].

Difference with the Canon Storyline
The whole Caesar Clown and Shinokuni story is omitted in favor of the dark dials story.
Wapol-Krieg Pirate Alliance ArcEdit
As the arc starts, the discussion between Luffy, Nami and Smoker about the Dials is interrupted by an enemy attack, and the group reaches a place resembling the Baratie Restaurant, where a strange alliance between Krieg and Wapol happened. After defeated them, Luffy meets Evil Franky, who attacks him with his Radical Beam. Luffy dodges it and then defeats the cyborg. Later, Kuzan appears on the restaurant, freezing the enemies, and Luffy flees away. Kuzan starts to talk with Smoker, warning him about the strange dark dials[6].
In the end, Franky returns to normal, and re-joins the crew. Then they talk again with Smoker about an alliance to save the other Straw Hat pirates[6].

Difference with the Canon Storyline
Smoker, Wapol, Franky and Kuzan do not appear during the Baratie Arc in the manga and anime series.
Wapol never reached the New World in the canon storyline. Also, this arc being set after the timeskip, Wapol should have quitted being pirate to become the king of Black Drum Kingdom.
The final chat between Smoker and Kuzan greatly resembles the one they had at the start of the Dressrosa arc, except that the subject is not Donquixote Doflamingo but the dials.
Stage 3: "The Legendary Marine" Garp ArcEdit
Garp appears and requires Luffy's Trembling Dial, the only thing that can counter the Fog Dials' effect. Luffy and Smoker's group goes against him and they have to fight Garp's division. During the fight both Borsalino and Jinbe arrive on the island[7].
At the end, Luffy, Nami, Franky, Smoker and Jinbe decide to go for the Sea of Fog, to search for more information about the Fog Dials.

Stage 4: Thriller Bark Arc
The group lands on Thriller Bark and starts to fight against the zombies. During their run for the mansion, they are able to defeat and free both Brook and Tony Tony Chopper from the Fog Dials' influence[8].
Once they reach the mansion, Gekko Moriah appears and, after a short fight, he summons other zombies, which Jinbe purifies with a huge water column. Moriah then absorbs some shadows and tries to attack him, but the Fishman defeats him with his Fishman Karate[8].

Back on the Thousand Sunny, the group starts to talk about Luffy's missing crewmates. Smoker claims that Punk Hazard should be protected by the World Government now, and their force is not enough to come back there. Then Portgas D. Ace appears, claiming that his father wishes to see Luffy.

Difference with the Canon Storyline
In the game, Perona and Moriah are still in the Florian Triangle after the timeskip, while in the canon storyline they're not.
The presence of zombies suggests that even Hogback is still in Thriller Bark. However he does not appear during the stage.
Jinbe defeats Moriah and his zombies the same way he did during the Battle of Marineford.
In the game neither Absalom, Hogback nor any of the main identifiable zombies appear.
In the game both Ace and Whitebeard are still alive after the timeskip instead of having died at Marineford.
Stage 5: Whitebeard Arc
Luffy meets Whitebeard and Marco and the rookie declares war to them, then attacks the Yonko with an Elephant Gun, but Marco intervenes. After the fight against the Whitebeard Pirates, they agree to help Luffy to search for his crewmates[9] and the two crews form an official Pirate Alliance. In the meantime, Ace continues his research of Marshall D. Teach.
Difference with the Canon StorylineEdit
Whitebeard and Luffy's first chat follows the one during the Battle of Marineford.
The Whitebeard Pirates and Straw Hat Pirates officially form a Pirate Alliance, while in the canon storyline, Luffy's first Pirate Alliance is with the Heart Pirates.
Stage 6: Return to Punk Hazard ArcEdit
The new Pirate Alliance arrives to Punk Hazard and the playable character runs to the ice side of the island, fighting Marine soldiers along the way. Suddenly, Rob Lucci appears to defend the base. After his defeat, him and the player character reaches the fire side of the island, then Akainu arrives[10].
The group talks with Kuzan, who suggests the truth behind the Fog Dials could be in Impel Down[10].

Difference with the Canon Storyline
In the game, the CP9 is still working for the World Government after the timeskip, and has been dispatched to Punk Hazard.
In the game Magellan is still the Warden of Impel Down.
Stage 7: Arlong-Crocodile Pirate Alliance Arc
Difference with the Canon Storyline
No Arlong and Crocodile Pirate alliance exists in the canon storyline.
Crocodile never went to Arlong Park in the canon storyline.
Stage 8: Impel Down Arc
Stage 9: Marineford Arc
Stage 10: Sabaody Archipelago Arc
Difference with the Canon Storyline
Enel never landed at Sabaody Archipelago in the canon storyline.
Stage 11: Baratie Restaurant Arc
Stage 12: Alabasta Arc
Stage 13: Return to Thriller Bark Arc
Stage 14: Orange Town Arc
Stage 15: Enies Lobby Arc
Stage 16: Drum Island Arc
Difference with the Canon Storyline
Enel and Borsalino never met each other in the canon storyline.
Borsalino was never seen visiting Drum Island in the canon storyline.
Enel never reached Drum Island nor the Blue Sea in the canon storyline.
Stage 17: Summit War Arc
Difference with the Canon Storyline
While in the canon storyline Whitebeard got killed by Teach and his crew, in the game he got killed by Moriah's Tsuno Tokage.
Teach absorbes Whitebeard's Gura Gura no Mi while covered by Moriah's Black Box, while in the canon storyline he is covered by a black sheet.
Teach never defeated Sakazuki in the canon storyline, where he even escapes from him.
The scene where Ace is almost killed by Akainu resembles the one where the Admiral actually killed him in the canon storyline.
In the game, Garp chooses his family over the Marine and wishes to save Ace, while in the canon storyline the opposite happens.
Stage 18: Blackbeard Final Battle Arc
Difference with the Canon Storyline
An original ending of the fight against Blackbeard is given, while in the canon storyline it has yet to start.