It seems similar to this problem Micro freezes with Relive enabled in bf4 and bf1 which was fixed in the past.
I used to be able to record the game just fine with plenty of both CPU and GPU resources to spare. Then after a long time not playing it I tried again and now it has this stutter problem . It makes it completely unplayable.
Because of this problem I did a clean windows installation and tried all kind of possible fixes, making sure windows DVR recording function is off for example. I have nothing else installed in the system, not even antivirus. I wanted to make sure nothing else was causing the problem. It is Relive causing it for sure. Temperatures for both the CPU and GPU are under 70ºC.
Using the performance monitoring included in Radeon I can see that when I start recording the GPU "throttles", because instead of being at a somewhat constant percentage of usage it goes down to 5% usage, even to 0% usage...
Windows 10 - Version 1803 - Build 17134.228
Latest stable Radeon drivers - 18.5.1
Rx 480 8gb Nitro + OC