All I had to do was slip a razor blade between it and the body of the mouse to cut the glue. I was then able to pop the top of the mouse off the hinges on the bottom, unscrew the “scroll ball” assembly, pop off its top cover, and clean the rollers. I’ll have to glue the retaining ring back on with a couple dots of superglue, but the mouse works fine without it right now.
Update: Four drops of superglue, and everything’s back together and working perfectly. I’ve also crossposted this over at MacHELP.
Note: I took my Mighty Mouse apart after all the other cleaning methods had failed. I tried all kinds of cleaners, scrubbing the ball, etc, and it had gotten to the point to where taking it apart to clean the ball rollers was the only option.