Yes I am using the Skyrim HD 2K texture mod, but like I said, I tried just vanilla Skyrim and the same stuttering still occurs.
The problem you describe is the same that running out of VRAM would cause. It's a little laborious but try this.
Delete all texture files or mods you may be running.
Revert your ini files to default (if you've changed ugridstoload then you need to follow specific instructions to change it back to 5).
Uninstall and reinstall 12.1 (also try intalling 11.11c instead)
Ensure no program's are running in the background besides steam and your AV.
If all this fixes it, add your mods/ini changes one by one and maybe you'll find the exact cause.
Quick edit: First try disabling crossfire.