I'm going to guess that what you're talking about is streaming your game screen online while you play, and that you're asking if you can clone the display with different resolutions, so you can duplicate the output to a capture card that accepts 1080p, while still playing at 2560x1440.
I very much doubt anything like that is possible. A duplicated display must be the same resolution from what I can see.
You're not going to find any consumer grade capture hardware that handles that kind of input resolution.
Your best bet is to fiddle with the software you're using to see if you can reduce the load, or try another package altogether.