I recently purchased the Apple Mighty Mouse, which by the way is one of the crappiest pieces of computer hardware I have ever purchased, and the scroll ball wheel stopped working after only a few months. After doing a little bit of research, I noticed this was happening to many other people along with me.
I searched the web and found some helpful articles to assist anyone else who seems to be having this problem. Below I have some tips and pointers of my own, and a bunch of links that should help fix the problem. I was going to write my own article on how to fix the scroll ball, but all of the articles are there so why bother?
This is probably the best process to go about cleaning the mouse:
Note: Talk to apple first and see if they will just replace the mouse for you!
1. First just try holding the mouse upside down and rolling the ball around, sometimes that helps to dislodge particles that have gotten trapped down inside the wheel’s cavity. You may also want to try spraying some air at the ball and in the cracks as you roll it.
2. If that doesn’t work, or if it does only for a little bit, I would suggest trying what I ended up having to do. Try using a cotton swab and roll it around the ball vigorously (without liquid of any kind), that helped a lot for me but only lasted a few weeks. You could also try using some isopropyl alcohol or another similar product, but I would try the following idea first before you introduce chemicals.
3. I found another great idea and an article to go with it about using a thin piece of tape to collect the particles that have lodged in the scroll ball. They say to put the sticky side down, but after taking apart the mouse i realized that the problem is not the ball itself, but the rollers that it rides on (The little white things in the picture below). Thus, if possible, it would be better to put the sticky side of the tape facing away from the ball. (You’ll know what I mean when you read the article). Here’s the link to the article: Link

4. If none of those ideas work, you may have to take the mouse apart. Be careful, a lot of things can go wrong if you don’t do it correctly. I would just suggest not taking it apart at all. Heres a good article on how to do it: Link
When my mouse’s wheel jammed up for the last time I ended up having to take the mouse apart which was a project of it’s own. Absolutely do not take the mouse apart unless you have to. It definitely will do a great job to fix the scroll ball problem, but you will end up with more problems trying to put the mouse together. The plastic ring on the bottom of the mouse has to be removed to put the side pieces back in, and it is very hard to do without cracking the ring.
All of the methods and techniques I have shown you are on the web somewhere (except for maybe the cotton swab idea, that was mine =D), but now they are all together in one spot, step by step. I hope this helps.
**Disclaimer: If you break your Mighty Mouse, it’s not my fault.