Since every mouse is different, this hack is mainly about the idea. If you can operate a tiny screwdriver, you should be able to do this whichever way your mouse is put together.
1 computer mouse
1 #00 Phillips head screwdriver (small)
1 X-Acto or utility knife
I am going to do this with both a Logitech USB Mouse and an HP Wireless Elite Desktop Mouse.
Step 1: Find how to open it
Under pads: using an exacto top, carefully pry these up and keep in a safe place to reattach later.
Behind stickers: rub your philips head screwdriver over the sticker looking for indentations. These indentations may be a sign of a hidden screw.
The logitech was simple: one screw and the whole thing came apart. The HP will take some tricky moves...
Step 2: Pry open the case
Be very gentle, you don't want to break off any of the plastic tabs in the process.
So now that both cases are open, we can look inside.
Step 3: Identify wheel mechanism
The Logitech's spring is right in the middle of the wheel (already removed in picture) and could not be easier.
In an HP Wireless Elite Desktop mouse, the easiest access to this wheel's spring mechanism was right on the top of the mouse underneath the buttons. I was tempted to disassemble further, but they made it rather tricky. Not wanting to break the thing I chose a different method–remove the notches from the wheel.
Step 4: Remove Spring
Remove it and you are done. Congratulations!
Step 5: Scrape off the notches
I suggest holding the blade against the notched wheel at a 90° angle to the notches you would like to remove and spinning the wheel with your other hand. Continue until there are no more notches and the wheel is smooth.