Gods of Destruction possess the power to destroy almost anything with little effort, even working on intangible beings such as souls in the anime. People destroyed by the Hakai do not go to the Other World and simply cease to exist. However, in the manga, Beerus admits that Hakai does not work against immortal beings.

Who does hakai work on?

Hakai (破壊 'Hakai', lit. "Destruction") is a powerful ability used by the Gods of Destruction. In the manga, Goku is also able to use it.

Does hakai destroy the soul?

However, in the manga, Beerus admits that Hakai does not work against people who are immortal. Since the Other World is their equivalent to our afterlife where presumably, our ghost or spirit goes after death, then yes, Hakai can destroy someone including his/her ghost/spirit.