It does not have to be related to sounds specifically, on my main gaming uber-rig, I have no stuttering at all, while on laptop, I have it all the time.
There are many assets required to display the fighting animations - animations themselves, textures, sound effects, and they can be stored on various media with different access speed - hdd, ram, VRAM. What is desirable in what situation may be different on every configuration, sometimes VRAM is just too small, and the video card bus slows down the process, sometimes there is not enough RAM and disk must be used frequently. Optimization is no easy task.