OP, have you tried unplug, wait a few minutes, plug it back in again?
I've long believed tvOS has some kind of memory leak/hog bug that eventually eats up almost all available RAM, leading to issues like stuttering. I do this cold reboot once each month which often results in smooth operations and no stuttering.
I suggest also doing some simple things to try to pin down the issue. First on my list is get a run of ethernet long enough to connect by ethernet (router to AppleTV), then watch for a while and see if you can see the stutter. If not, you may have wifi issues. Since it seems random, are others tapping the same wifi bandwidth during stutter periods? Have you shared your password with perhaps neighbors who may be inadvertently tapping your wifi instead of their own? If you are not sure, change your wifi password to kick anyone around you OFF your wifi.
If the ethernet connection yields no stutter, disconnect again and watch for stutter in something. If it returns, immediately pause what you are watching, reconnect ethernet, back up what you are watching a bit and resume across parts that just stuttered. Smooth this time? If so, that increasingly says you have wifi issues- a very common cause of stuttering video. IMO: unless it is the ONLY possible choice, I don't think AppleTV should be connected via wifi. Streaming video hogs too much bandwidth and can lead to what you are seeing.
Is the content you are trying to watch formatted for AppleTV or is it trying to be converted on the fly? That could cause stutter.
Are you air playing this content to AppleTV or seeing stuttering while using AppleTV apps?
Can you make some content stutter EVERY time you play it on AppleTV? If so, put a MB in the same spot as AppleTV and play the exact same video by the exact same method (wifi or ethernet). Does it also stutter on MB? If it does on MB, that again suggests wifi or perhaps even the content itself, source of content, not robust Internet connection, VPN in play and clogging up the flow of signal, etc?