Definitely not the card then. I don't really have any solutions I'm afraid, but it does seem a bit odd.
I run a 1080, i7-8700k, 16GB memory and the game is on an SSD. My monitor is set to 120hz but I use GTA Vsync on half which pins the game at half the refresh rate... 60FPS. If I turn Vsycn off it will do a lot more than 60FPS but that fully loads GPU which causes more fan noise than I like and introduces the occasional noticeable stutter when FPS jumps around.
I run everything pretty much max apart from the grass (because it crushes performance and I can't see much difference between high and ultra) and the anti aliasing settings because I found max != best. For example 2x MSAA with TXAA on seems to give me equal results and better performance than running 8x MSAA alone... but image quality and what is "playable" is a very individual thing.
Other things I noticed is that for some strange reason playing in full screen mode (not windowed or windowed-borderless) improves stutter and seems to reduce the load on the GPU.
If the game is on a slow HDD that could be it. Otherwise it looks like some kind of driver or software conflict issue. It might be worth adding GTA to your anti virus or windows defender list of excluded programs. Maybe try running the game with no other programs running on the pc at all and making sure all overlays like afterburner/steam/shadowplay/etc are completely disabled.