If you have an nvidia graphics card and the latest drivers, go into the nvidia control panel -> adjust desktop size and position -> change the dropdown menu where it says "Perform scaling on:" to Display.
This sounds like the exact problem I was having, where I had anywhere up to 140 fps but the game was still stuttering. Turning off the new scaling feature on the nvidia drivers using the steps above worked for me; if it doesn't work for you try changing some more of the settings on that page, e.g. change the scaling mode to Full Screen or No Scaling, and turn off "Override the scaling mode set by games and programs".