Your computer mouse is like any other electronic device in that moisture spells trouble. In general, if you spill a drink on your mouse or any other electronic, you need to move quickly. Irreversible damage can occur quickly. Also, you may ultimately need to purchase a new mouse since your efforts may not be warranted for the amount of money that you can spend on a mouse these days.
Unplug the mouse from the computer. This is extremely important because liquid and electricity is a dangerous mix. It also makes it easier to work on your mouse when it is unplugged.
Wipe it dry with a rag or towel. Do this as quickly as possible. You may be able to save much of the moisture from creeping inside of the device if you move quickly.
Take the mouse apart with a Phillips screwdriver. The object is to expose the inside of the device to air.
Turn on a fan and lay the mouse next to it. Air drying devices is a good solution. Let the fan run for several hours.
Check to see if there has been any blue or green powder substance forming around any of the circuitry. If so, that means the device has started to corrode.
Re-assemble the mouse and plug the mouse back in to the computer to test it.