Isopropyl alcohol. Preferably 95% but I've done this with the typical 70%, so whatever you have in your medicine cabinet. With Mouse unplugged (powered off, battery removed for wireless mice,) put the mouse on a paper towel and pour a small amount of alcohol over the ball. What you are trying to do is get some alcohol down past the ball and into the internal rollers, which have some gunk on them that you're trying to remove. Isopropyl alcohol will not corrode the electronics and will help loosen and break up the gunk. Roll the ball and pour a little more. Repeat a few times. You will want to let everything dry as much as possible before using. Thus pouring a small amount and not the whole bottle and not "dunking" the mouse in a bowl filled with isopropyl alcohol. Do that only if you get really desperate, but if you do, then let it drip and air dry afterward.
There is not much space for the gunk to be "flushed" out so eventually this may not work. At which point you can look on Youtube and see several tutorials on disassembling the mouse. The mouse is glued together so this is not without risk. You may end up just buying a replacement mouse so just be prepared before attempting disassembly or even the alcohol.
(In case you're concerned, isopropyl alcohol has been used for cleaning around electronics for many, many, many years. Used to clean water/syrup/milk/juice damage since it doesn't corrode the circuit boards. While it generally doesn't conduct electricity, it was generally discouraged to use it on live equipment for various reasons. And due to skin irritation, gloves often were used, but in this case with the mouse and the small amount being used, it's up to you to whether you want to use gloves and eye protection.)
