Turn off iPad 2 screen mirroring I want to watch a video on youtube on my TV, connected with the HDMI adapter and a cable, but use other apps at the same time on the ipad's screen. I think this is possible if I use Airplay (to Airplay a video in the background), but I don't have an Apple TV, so i'm assuming it must be possible to play the video over the HDMI output while using apps on the screen. 

But when I switch apps Screen mirroring kicks in and the video stops playing, if I press play in the multitasking bar I only get the audio of the video.

Is there a way to turn off screen mirroring on the iPad 2 when using HDMI?
Sorry, no, it's impossible to run HDMI video out in the background while doing other tasks.  AirPlay, however, allows this with Apple TV, which you mentioned that you didn't have.  The HDMI out is strictly mirroring only.  Sorry I was unable to help you further...