I don't know if this will help anyone with these particular games, but I was getting weird stutters in Call of Duty 2 and 4 on my Mac Mini and it seemed like there was a correlation to hard drive activity (loading something new while playing would be when it would suddenly stutter for a moment). I have a RAID0 setup (which you would think would be better since it's faster) and by testing with a regular drive, I found the problem was worse with the RAID drive and that confirmed the hard drive (or driver) had something to do with the stuttering (not the GPU, which when it was not stuttering was completely smooth).
I found a suggestion on a Diablo 3 forum to get rid of hard drive related stutters (supposedly Diablo 3 is just awful in this regard, especially in multi-player; I don't know since I don't have the game). But I took their suggestion and tried with Call of Duty 2 and 4 and they are now 100% stutter free (just like users reported with Diablo3).
The key is to get a good sized USB thumb drive (they were using USB2 models, which makes even less sense when you consider the speed constraint, but apparently the stutter is not due to absolute read speed) and then copy the game folder over to that drive and run it off the thumb drive instead of your hard drive. They claimed Diablo3 was then magically stutter free. Many called BS on it, but others confirmed it.
I was in need of another thumb drive anyway, so I figured I'd try it out with Call of Duty 2 & 4 and so I bought a SanDisk 32GB USB3 thumb drive (much faster than a USB2 one, although still slower than my RAID0 setup; although random access may be better) and loaded them onto it. They are both now 100% stutter free. No more audio cutouts or frame pauses. It's SO much better. Since the saved games are still in the home directory somewhere, I don't even have to worry about copying back any data when I'm done. I can just erase the thumb drive folders and put something else on there and copy them back again if I want to play them again at some time in the future.
This may or may not solve your problems with various Blizzard games. It depends on what is causing it, but seeing as this supposedly fixed Diablo 3 for a bunch of folks and it certainly fixed Call of Duty here, it may be worth a try, particularly if you already have a thumb drive lying around.