Guys, guys! I've just fixed the stuttering by going offline in Steam friends. That's crazy I know, but I saw a guy posted this on Steam forums and this was the only thing that fixed the stuttering for me. I have tried everything before and it was stuttering every 3-4 seconds.
The guy said it happens if you have lots of friends on your Steam list and the game tries to update something constantly. I had 1000+ friends and he had 800.
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+1 This worked for me.