This is a driver issue. Report it as a bug and hope for a fix.
So I have a strange problem.
As I stated in the title, my screen lags if one of my monitors is off but both are still connected to the GPU.
The thing is, it only lags/stutters if one of them is off (it doesn't stutter if both are on)
As I often use my TV to watch movies, series or even play some games that don't need keyboard for me to play, I don't need the monitor to be on so I turn it off.
Then I get that annoying problem and I can't seem to get rid of it.
Also, my mouse lags (it just randomly stops for a second and then keeps on going) on movement if one of the displays is off (it doesn't matter which one, it happens on either one of them).
The problem goes away if I unplug the HDMI cable from either one of the displays.
The problem with that is that I always have to go under my table to plug in or unplug the HDMI cable, if I want to use the monitor.
That became very annoying since I payed for the privilege of having two HDMI ports on the GPU.
I have tried everything, changing the HDMI ports on the TV or the monitor, changing the HDMI ports on the graphics card
One more important thing, my monitor has 1ms response rate and is 75Hz, my TV is 60Hz, both are 1080p displays.
Could that be why is this happening or maybe there is a problem with my graphics card?
All my drivers are up to date, I use the RX 580 8GB from Sapphire and run Windows 10.
Thank you all for the help in advance!

Chowhound
Comic Vine
GameFAQs
GameSpot
Giant Bomb
TechRepublic