You can use mirroring, but TVs generally have a lot of overscan. You'll end up with a shrunken image on your monitor just to keep from cutting off the image on the TV.
I have a 770 and I have a dual link dvi hooked up to my 144hz monitor, and HDMI to my shitty 30hz 720p TV.
At first I was having weird resolution problem. What I ended up doing is disabling the TV through my nvidia drivers. So if I want to watch a movie on my TV, I just re enable the TV and press play.