How to open and clean mouse of iMac Bondi 1999?

They do need to be cleaned rather frequently.

To my knowledge you can use any USB mouse with that iMac, and if it were mine I'd use an optical mouse. No moving parts. I believe I eventually used a wireless optical mouse (Logitech I think) but it needs 2 AA batteries. They obviated the other limitation of the original USB Mouse — a tail that was too short.

Apply enough finger pressure on the grooves to rotate the cover about an eighth of a turn counterclockwise, and it will open.

https://www.youtube.com/watch?v=a7K60coooGU

For the cleaning part, wipe it with a microfiber cloth to remove any dust. You can also use isopropyl alcohol to clean it.

Lacking any "north up" orientation the original USB Mouse / Bondi Blue mouse counts as one of Apple's dumber ideas in my opinion. They quietly compensated for it in the subsequent model shipped with the "five flavor" iMacs with a more prominent finger groove giving the user some tactile indication of how to grasp it. It wasn't much of an improvement.

There was even a company that made an add-on housing that snapped on to the south end of the mouse, giving it an unmistakable, more mouse-like shape. It was called the iCatch — see what they did there?

Five seconds is all you need: https://youtu.be/a7K60coooGU?t=557