By 'stutter' I assume you mean start/stop abruptly.

Does the song stay in time, or does the 'stutter' cause a break for a short period of time and the song resumes streaming where is was after the last heard sample?

Another way of asking; is the audio signal getting interrupted but otherwise the song plays normal (in time, but just the audio cuts in/out), or is the song getting short pauses in the tempo and flow as a result?

The difference is a clue as to whether the audio signal is getting interrupted before or after the device drivers start handling it.
It could be an unsteady flow of data to the device or it could be a problem with the device drivers, or even resources. Maybe the CPU is hardly working but the hard drive is over taxed (causing the aforementioned unsteady flow of data to the device in the first place).
As mentioned above, a sample recording would help narrow it down.

Make your sound your own!
.. I do not work here, but the benefits are still awesome