Thank you for your question.
We are not a law firm - but a site that provides (among other things) legal information to people, therefore we cannot help you with possibly removing the comment.
I am not surprised that Yelp would not remove the comment. They generally only do so if it violates the terms of their service (e.g., there is foul language in it). About the only thing a business owner could do otherwise -and I am sure you know this - is write a polite response stating that the review is false and why it is false, and of course, try to get as many good reviews as possible, which will then make it more obvious that the bad review is not very credible.
If you knew who the person was who left the review, theoretically, you could sue the party for defamation
if you can show injury to your business. Such cases are normally taken on contingency, meaning you only pay if the lawyer is able to recover money for you. That said, most lawyers aren't interested in taking on such cases unless the damages are potentially significant (for example, a celebrity or public figure who has a damaging, false story run about them in the tabloids). It isn't otherwise worth the time and expense of a firm to file a lawsuit for a small recovery.