There are many, many threads regarding this issue. Check them out for more information:
https://us.forums.blizzard.com/en/wow/t/wow-classic-mouse-over-stutter
https://us.forums.blizzard.com/en/wow/t/right-mouse-not-working
https://us.forums.blizzard.com/en/wow/t/right-mouse-button-again
I’d just like to add something that many people leave out in these threads:
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The right-mouse button is by far the most used switch on a mouse when it comes to WoW.
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When mouse button switches start to fail, they do so intermittently because the little spring in the switch wears down over time.
So, therefore, a mouse with a failing switch - most likely the switch on the most commonly used button - will stutter and fail intermittently for a long time before the switch actually “dies” and becomes non-functional.
Do with this info what you will. You can test the theory by pushing down on the right mouse button really hard when it’s doing the stuttering thing to see if the problem resolves.
This right-click-stutter has happened to me many times over the years. I used to solve it by opening the offending switch and re-tensioning the micro-spring. There are YouTube tutorials on this, and they do work.
At times when I didn’t have the funds to buy a new mouse, and didn’t have the information needed to re-tension the micro-spring, I bought myself some extra time by wedging a tiny bit of paper or tape (equal to about two sheet’s worth of thickness) between the switch and the plastic piece that presses down on it. This gives the mouse that tiny bit of extra force it needs to press the switch properly.
Nowadays, I just get a new mouse, though. Not once have I plugged in a brand-new mouse and had the problem persist.
Good luck!