Thanks for confirming. Followup question: how long is the HDMI cable run to your TV? The distance of the cable run matters because HDMI signals can only travel so far before getting degraded.
I’ve seen this scenario when setting up the A/V gear for a corporate powerpoint presentation in a big conference hall. The projector at the very back of the room wasn’t projecting because the long HDMI cable running from the front of the room to the back degraded the signal too much. An active HDMI repeater / booster was used to alleviate in this instance
Also: is your computer’s graphics processor fairly high spec? If your GPU isn’t up to the task of pushing pixels quickly enough to refresh two screens simultaneously, that will also cause the symptom you describe. If disconnecting the big screen solved this problem, the GPU might be the root cause here. To check this theory - try reducing your display output settings in-game to the next lower setting.