For the 60FPS problem, it is due to the monitor's refresh rate. Say you cap the fps to 60FPS. As long as the FPS stays at 60, then a new image will be rendered for each refresh of the monitor.
However, if the GPU fails to do 60FPS, then the monitor refreshes before a new image is ready so it displays the same image. This new image will then be displayed on the next refresh on the monitor. This effectively means that the monitor has refreshed twice by the time the new image is displayed, so 60Hz /FPS becomes 30Hz / FPS which is why it seems to stutter.
I am not sure why you get this problem above 60FPS, as each time the monitor refreshes the new image is ready / 2 new images have been rendered so the 2nd is displayed...
What resolution and settings are you using? As maybe the GPU is running out of memory, bottlenecking the system.