I think the trick would be to realize that the texture on the mirror or portal represents the same screen height and position, just at the virtual screen location of the mirror/portal player behind it. So you render the screen space column as the flipped/mirror column but move the camera, avoiding overdraw, and use the fact that back faces on the wall/mirror texture are invisible from out-of-bounds. Something like that.

If you can lie to the engine and say that the flipped/portal camera is still inside the sector that the player is in (even if that's clearly wrong by the camera coords) then maybe your engine culls walls/floors/sprites not visible and you don't need to reserve an empty void for the mirror/portal camera to render from, so that level geometry can occupy the back side and make the illusion convincing.