Before doing anything else, turn VSync off, start a game, and type "/fps" into the in-game chat. An fps counter will pop up in yellow at the top-right corner. Do whatever you were doing when the stutter happened, and check the fps. Most likely your FPS is dropping below your monitor's refresh rate (probably 60), and when that happens with VSync on it cuts the framerate in half[*]
, which is probably why you get stutters.