When I used to have to fix these on the regular (having one at home AND having to do the tech support for them at work), just cleaning the ball on the outside was never enough, and I needed to reach inside to clean the rollers underneath the ball. I tried all sorts of things but found the best “tool” for the job was a plastic fork with the outside tine flattened (yes, I used my mouth to bite it flat). It was thin & flexible enough to wrap around and fit between the ball & the rollers but firm enough to actually be able to scrape the gunk off of the rollers.

I hope this helps! (Gotta admit, I prefer this mouse to the Magic Mouse.)