I had a similar problem a while back which caused me to switch to Wayland, at least to wait until the problem went away. Once I made the switch I no longer had stuttering on the entire desktop, but it still happens in some games. For example there is no stuttering in Minetest, but there is stuttering in Xonotic.
In my attempts to track down the cause I've seen some bug reports concerning recent versions of SDL which attempts to do something like enumerate joystick devices every 3 seconds and causes a mini freeze. Does your stuttering occur at regular intervals around 3 seconds as well? If not then maybe this is unrelated to your issue. If it is the same issue then I recently found a temporary workaround which is to re-write packages and their dependencies to use SDL version 2.0.8.
