Games and a "stuttering" on SSD + HDD

Question

my problem is a bit weird I guess... I have a pretty new laptop.

Specs: Windows 10 Home, Intel i7 - 7700 HQ (2.8 to 3.8 GHz)

16GB of ram

G-Force GTX 1070 - 8GB GDDR5

And what I think might be the most important, 2 storages.

256GB SSD and a 1TB HDD (7400 RPM)

All my game launchers are on the SSD, while most of the games are on HDD. For example, Steam and Battle.net are on the SSD. I have Hellblade installed on my SSD and it works perfectly, even at very high details. However World of Warcraft and other games are on my HDD and they have this weird "stuttering". I use parentheses, because I'm not sure if it qualifies.

Every now and then, the game goes to very low FPS, it's either stopping completely for a period of time (I'm literally talking fractions of a second, but just enough to notice) or it happens few times in a row (over a course of maybe one second). However after that period the game works perfectly again. And it seems that the game time "has passed". If I'm driving a car and the game freezes, after the tiny freeze I'm further in the game. Then it goes to perfect framerate until the next stutter (they can happen every 30 seconds for example?).

Now, what my research has shown:

Hellblade is installed on SSD and it has NO stutters at all, even at high details with quite high CPU / GPU temp

ETS2 (much less demanding game) was installed on HDD and had terrible stutters every 30 seconds or so. I looked it up, and it turns out that it was an autosave. I found a trick to run the game with special command line options and move some files between SSD and HDD (i forgot which way. If it's important, I will find out) and that has fixed the issue. There's still a tiny stutter when this happens but it's much less and I guess it's as good as it gets and that's just an issue with the game itself.

World of Warcraft and even rise of nations (this game is more than 10 years old now...) the game has a tiny stutter with every other sound effect or anything similar. That really indicates that the HDD is the issue?

It happens in WoW and Wolfenstein: New Order cutscenes too. And now the really weird thing - during those freezes, sound usually works perfectly, but graphics freeze. I don't have any problem with internet, watching pictures and listening to movies - or even coding or using Virtual Machines.

I checked the CPU and GPU temps on every of those games, and Hellblade is the highest but ironically it's the only one that works fine. I checked the HDD with defraggler - health is "Good". Read and seek error rate = 0

It really seems like the problem was installing the game launchers on a drive other than the game itself... does anyone have any advice or opinion? Is there some kind of setting in BIOS or anything else I can do? I forgot to mention - the built in screen has G-Sync. Maybe I should / could change some Vertical Sync options... That really seems a hit and miss with every game though. I really think it's the hdd issue...

Thank you very much in advance. The problem isn't a huge issue - but it's incredibely annoying.

EDIT: a commenter asked about my hard drive type. The exact name is:

HGST HTS721010A9E630

I checked the website for it. I don't know if it counts as a Green Drive but it says:

Low power consumption Halogen-free for eco-friendly design

Is that the problem? If yes, can I do something about it?