Let’s take things step by step. We’re talking about the strongest swordsman in the world, Dracule Mihawk. We all understood his awesomeness when in one of the first episodes he slashed and beat Zoro so easily, using just a little knife.
He also trained him years later, in the two year gap of the time skip. That’s what we do know regarding him, but is there more to it? What is his role really? We haven’t seen enough, and that’s for sure. He certainly is a mysterious character.
His relation to the Straw Hats
It’s quite obvious that in the times he met members of Luffy’s crew, his moods against them weren’t exactly hostile. Zoro lost to him and later became his disciple. Mihawk didn’t kill him when he could. Moreover, in the War of the Best he attacked Luffy, but it seems it was just a way to test his strength, and not really an attempt to kill him. The pattern is that he either wants the Straw Hats alive or at the very least is interested to see the potential they possess.
Blackbeard Pirates vs Red Hair Pirates
A battle that was basically foreshadowed at Marineford is the one between those two crews.
Why is this related to Mihawk? There is a possible hint that Oda has given us when Shanks’s crew was revealed. In the War of the Best we saw 10 members of the Red Hair Pirates and 11 of Blackbeard’s crew. If it is intended for us to watch a one on one battle, it could be that one secret member is missing. Can that crew member be Dracule Mihawk?
He has no crew, no pirate flag, no real ship even, yet he is considered a pirate by the World Government. There is a possibility he was part of the Red Hair Pirates. He decided to leave them before Shanks was a Yonko, in order to become a Shichibukai, an insider in the World Government working for his captain Shanks.
I think Shank’s goal is to maintain balance in the world either indefinitely or until Roger’s successor challenges the world to a fight. All of Shanks actions point toward this. His four big moves have been, trying to stop Ace and Blackbeard from fighting, halting Kaido, stopping the war, and of course appearing in Mary Geoise to warn Gorosei.
So Shanks could have sent Mihawk, his former crewmate, to become a Shichibukai to help maintain this balance.
Mihawk’s relationship with Shanks
In the past, they sought out each other on many occasions to duel. Their battles were said to echo through the whole Grand Line.
However, Mihawk has given up on trying to fight Shanks after he lost an arm. He retains a neutral, though a somewhat friendly relationship with Shanks, and can track him down if the need arises.
Furthermore, the way Shanks asked him to party with his crew, resembles the way a captain would go about treating a crew member of his. Also, when Shanks made his entrance during the War of the Best, Mihawk left the battlefield while stating that he agreed to participate in the war against Whitebeard, but fighting “Red-Hair” is beyond the scope of the World Government’s orders.