I don't see a second floor, so I will assume that it will be new. I also don't see the staircase, so I assume it will go where the red box is shown. Why do you need to cut the member? Can the staircase simply bear against the red member rather than going thru it?
What other loads are on the red section that we are not seeing?

Second floor is grey area in rendering. (in Europe = 1st floor)
Approximate staircase position and landing shown in new image.
The reason to cut through the lower joist, is that distance between bottom and top joists is about 160cm, - terrible for bumping heads.
The loads on the bottom joist: i assume it is well connected to exterior mortar/walls to avoid bowing of walls. You can also see central poles resting in centre of lower joist, stress which is distributed downwards through smaller vertical poles and a wall on the far side.



Image from inside perspective looking up (lots of misc. wooden structures to be removed)

Its difficult to see the function of that member. It does not appear to be part of the truss. The only gravity load on it appears to come from the post above next to the edge of the masonry wall. Perhaps it serves as a tension tie to prevent lateral spreading of the exterior walls. You may want to create a model and look at the end connections of that member to convince yourself what that member is really doing.

I am quite sure it serves as a tension tie to prevent lateral spreading of the exterior walls. I'm just wondering of the possibilities/effectiveness of connecting it to the mass of the parallel wall below its length.