Am on LMDE6 with an ancient Nvidia card. Because I've had to resort to using the Nvidia OEM driver installer (which can be a pain to use), installed Xorg updates lurk quietly until a full reboot at which point they generally cause offloading of GPU tasks to the CPU instead because it hasn't figured things out properly.
Timeshift has been useful at least twice in getting me back to a less stressed system.
I think I have a procedure figured out now though (documented here for posterity even if it helps no-one today):
Make a Timeshift snapshot just in case
Install the pending Xorg update
Reboot so it's fully active
Check to see if GPU tasks are being offloaded to the CPU by doing something graphics intensive and noting temperatures or usage%. If not, a miracle has occurred and continuing isn't needed.
sudo remove the execute permission on /usr/bin/Xorg so that it can't immediately be restarted by subsystems designed to protect the average Mint user from command lines and consoles.
Kill Xorg
Log in through a console, via Ctrl+Alt+F1 or similar if not dumped to one by killing Xorg.
Re-install the Nvidia OEM driver
sudo put the aforementioned execute permission back on
Repeat steps 2 and 3 and hope that this time the GPU is doing the work.
Reboots ought to be replaceable by running specific commands, but I haven't gone deep enough into things to know the right things to do there. Reboots are quick and easy enough.
Obvious intermediate steps include not doing anything else important during this and saving important work before starting.
e.g. did you know it's possible to bookmark all open tabs? Well worth looking into.