This appears to be a memory related issue
After playing on the XBox One for more hours than I care to admit, this problem appears to be memory related. Specifically, the more time is spent playing the more likely that this glitch occurs.
In my experience, the only fix that is needed is to close the game from the start menu. That will clear the memory. I have never seen it corrupt a save, so saving or quick saving, stopping the game, then immediately restarting has always fixed the problem.
I have not experienced any difference with this with or without mods, except that many mods cause a CTD which ends up, of course, clearing the memory. As such, I've found that any mods that cause consistent crashes tends to prevent this, but only coincidentally.
On the other hand, purposefully causing this is disturbingly easy. I've found that switching to other applications while Skyrim is "running" (e.g. save, but don't quit the game, then switch to, say Netflix, then come back) tends to significantly increase the odds of this "stuttering" effect.
One note, while the above says that it only affects the sales, that's not quite correct. It's most notable in the sales menus, however, it tends to cause "stuttering" while moving and in combat, though the effect isn't as obvious (or as annoying.)