If you intend to use this as an egress, the hole must start above the nose of the step that is 80 inches below the floor joists. Then it would have to be as long as need to gain access to the top step from above. I would continue the stairs to the deck. If you are cuting 2 floor joist, I would run 2 new floor joists on each side of the hole nailed together like a beam Place temp. supports under the joists to be cut and cut the joist 3" back from what would be the ends of the hole then add a double header at each end to support the cut joists.
I would only make the opening 36" wide and add the double floor joist to each side for strength. I see you suggest 48" wide in that case you might just add one new joist along side the old ones.
Either way you want double joists on each side and a double joist, beam, or header on each end, and install the end peices with double hangers pick up the cut joist with single hanges. If the floor is a little bouncy after that you could add a post in the center of the span under the double joist as you do have a concrete floor.