In the world of One Piece, the potential outcome of a battle between Roronoa Zoro and Dracule Mihawk, also known as "Hawk Eyes" Mihawk, is an ongoing point of speculation and debate among fans.

Mihawk is widely regarded as one of the strongest characters in the series and is considered the greatest swordsman in the world. He possesses exceptional skills in swordsmanship and wields a powerful black-bladed sword called Yoru. Mihawk's strength and reputation have been established through his battles and encounters with other powerful characters.

On the other hand, Zoro, one of the main protagonists of One Piece, is also an immensely skilled swordsman. He constantly trains to become the world's greatest swordsman, just like Mihawk. Zoro has demonstrated incredible growth and power throughout the series, achieving numerous impressive feats.

However, it is important to note that the outcome of a battle in One Piece depends on various factors, including the characters' abilities, strategies, and circumstances. Additionally, the story's progression and character development play a significant role in determining the outcome of conflicts.

As of my knowledge cutoff in September 2021, Zoro has not had a direct battle against Mihawk, so it remains uncertain how a clash between them would unfold. The ultimate resolution would be decided by the series' creator, Eiichiro Oda.

It's worth acknowledging that One Piece is an ongoing series, and future developments and revelations may affect the dynamics of such a hypothetical battle.