No, you should never delete a negative comment on social media. Deleting a negative comment will offend your angry customer to leave more unhappy follow ups in your comment section, or worse, on your mentions.
Consider the negative comment a blessing in disguise – show the rest of the followers and the angry user how much you care about them by replying instantly. It will build up goodwill with them. However, if the posted comment is vulgar or threatening, feel free to delete it.