My radeon rx 570 8gb is stuttering on game as simple as GTA San Andreas BUT on something like Watch Dogs 2 it works just fine
temps are good under (50℃)
It stutters (cursor) even in the main menu before I even entered the game
I would start trying older drivers (or newer if you have older)
Mess with some settings like VSYNC, if its on one game only, probably its not the cards fault.
The latest adrenalin software also has a very comprehensive set of configurations that you can mess with.
My GPU in a very specific game screams out loud with coil whine although its an easy and very old game, I have to turn VSYNC on or Radeon Chill to keep it quiet. (for example)