What games? Is game set to render at 1080p 60fps? Is the GPU holding 60 fps? What does the GPU utilization and clock speed profile look like? Some software utilities (Razor Synapse) can adversely impact on software CPU affinity and PC performance. I've also seen 3rd party software that can mess/interfere with GPU clock states. Close all such utilities & any other software programs.
What is your monitor refresh rate? Test fixing to 60Hz, under Radeon Software test with freesync, enhanced sync, chill, FRTC, anti-lag all disabled, turn off ReLive.
What power plan are you running? Power saver can cause stuttering. Check if the High Performance plan helps.
Increasing GPU render ahead / Max Frame Latency / GPU buffer in game settings can help reduce stutter.