Thought I would share what fixed my long-lasting stuttering problem on GRID Autosport. (Lenovo G580, Intel Core i3-2348M @ 2.3GHz, Nvidia GeForce GT 635M, 4GB RAM, Windows 7 32-bit, single HDD, multiple partitions.)
1) Reinstalled Nvidia display driver 306.97 from 2012 (!) (https://www.geforce.com/drivers/results/50006) after sweeping the latest drivers off my system with Display Driver Uninstaller. 2) Cleaned the fan as much as possible (without disassembling my notebook) via a small hoover and using the Fan Dust Extraction feature of the Lenovo Energy Mgmt software.
Additionally, I'm playing Custom Cup only - when I started Career mode and returned to Custom Cup, the stuttering reappeared for some reason. I then reset career progress in the Options menu and it is now working again, so I suggest not even starting Career mode at first, if you play Custom Cup/Online/Splitscreen only. (Haven't actually checked if it reappears in Career mode down the line.) Graphics settings are near ultra low due to my rather outdated rig, and it DOES have an effect as well; raising them too much (relative to your specs, of course) brings the issue back no matter what you do otherwise.
This is confirmed to work on the same specs for another user with the same problem (although possibly with another title); I don't know if it works on other configurations as well.
But it's definitely worth a try for those who are in the same boat as we know it's a pretty uncomfortable issue to have - it plagued my system ever since I'm playing this game, which, as a result, I did so intermittently for the past three years now.