Hmmm, your original post may have given it away - "The stutter occurs whenever there is a radio message".
Go into the HUD settings and turn off the video feed during communications (the talking head). You'll still hear the messages you need to hear - just without the command/pilot pictures.
9 times out of 10 this will solve any gameplay stuttering during missions. I believe I read somewhere on this forum that the video messages play at a different frame rate than the game itself and causes some video cards consternation in the process (some handle the difference gracefully, others, no so much).
Give it a go and see how it works. I shut my video feed off ages ago and don't miss it a bit - and have never had stuttering issues since (and besides, the video feed can actually get in the way of your combat view sometimes).