Mention means to give highlight to. For example, if you mention a specific game in a gaming post, you give highlight to it. Refer may be either quoting information from something, or send to you someone based on your approval. For example, a general doctor could refer you to a specialist, or I could give direct reference to information from a biology book, in my blog on the human body. I’m not just highlighting the book, but using the information

"refer" implies approval. If I refer you to an employer, it implies I think it is a correct move for you and the employer to talk. "mention" is simply saying a name without a bias.