So recently I was looking some of my demos and I was wondering when I die in demo can I somehow remove black screen so I can continue watching what's happening?
I don't believe that this would be possible due to the demo recording your view point. The only way around this would be to get rid of the black screen when dying at all - but that isn't going to happen.
If you need the other viewpoint then I'd suggest asking the person who killed you for their demo so that you can watch it over.