Yup. Had one a number of years ago through the Princes Trust. I got a grant to start a business, and as part of that, I had to have a mentor.
The mentor was highly experienced. I was dubious, as his area of expertise wasn't in my business niche. However, it worked well and I was able to see how many areas of different business bits overlap. Plus, at the end of the day, a balance sheet is just that, weather you sell hosting or make your own cup cakes.
Also, having someone from outside the niche, it was useful to pitch advertising ideas at, and get their views on different bits and pieces.
It worked well, and I had a kick up the arse when needed, and a person to share the problems with, who understood what those issues were.
My mentor was a Doctor of business strategy, worked at top uni's in the UK and USA, ran some very successful firms, Google their name and it brings up hundreds of news articles on major news sites, now retired, and spending their day being a mentor.
But likewise, I have spoken to some people who's mentors sound terrible.