Constant stuttering

I don't know if this should be posted on this forum or not, but have no idea where else to ask about it...

I have an 7950 GPU, which runs the game perfectly fine.

I only have a 60Hz monitor, so I see no need to have 80-120 FPS in the game and have to hear the fans at higher speeds... I also get tons of screen tearing that way.

So I've capped my FPS to 60, but this have brought up an EXTREMELY annoying thing. My game keeps "stuttering" at a constant rate with 1 second between. I'm not talking about some minor stuttering here, it's very noticeable, and it's driving me crazy...

The most annoying thing is that I know how to fix all this, but that single solution I have, gives me another problem that I don't want to see either...

I read that others had stuttering problems too, and that it would get fixed with forcing v-sync and triple buffering outside of the game. Since I have AMD GPU, I can't use their official software(CCC), because that does nothing... but I found out about RadeonPro, which worked like a charm, I thought....

Using Dynamic V-sync worked wonderful, and if there was any stuttering, it was very minor.

After a while of using that, I noticed on my CPU core temperatures that one core was very hot, while the rest was at normal load levels... Turns out these settings make one of my cores get 100% load constant. (if I turn off that core, the next one will get 100% load)

I then tried using normal V-sync instead, and everything worked like it should, but... The stuttering was back. I noticed though that my FPS was fluctuating a lot (59-64), so I tried to lock the FPS to 60. That removed the stuttering, but I got the same problem with 100% load again....

I've spend hours and hours trying to at least reduce the stuttering while having normal CPU loads... but I just can't come up with anything.
There doesn't seem to be any other programs that work either.

Anyone who has any idea at all?