That's micro-stuttering, not the stuttering that happens when you move between places.
To fix micro-stuttering you can try to cap fps exactly at 30 (just to see if it's fixed). The micro-stuttering may depend on the fact the game internally has a clock that goes 30 fps, and so it handles poorly if you are above 30.
For example, if I cap framerate at 35, I get a lot of stuttering. Yet if I cap it at 30 the stuttering goes completely away.
I know that at 30 fps goes away. It's possible that also at 60 it goes away. Set your monitor at 60hz. Cap framerate at 60. If you go above 60 stuttering will show, but if you are at fixed 60 it should go away.
In my case setting the monitor at 60hz and capping framerate at 30 the stuttering is completely gone, whether or not I enable vsynch.