Originally Posted by joed
Without knowing the direction of the joists above it next to impossible to be sure.
Actually, the drawings that the OP supplied to show the main carrying beams, allow the viewer to assume the locations of the joists (based on modern residential building & construction design).
Couple that with the overall design of the house's footprint; the rafter/truss locations can be assumed as well. This allows the estimation of where (direction) the joists are running.
Again, that is based on viewing the PO supplied details.
However, no responsible person on this site, will tell a poster, to go ahead an cut-away, unless they could see the area in person. That would be irresponsible on our part. Thus, the best and safest method, would really be, to have a licensed or certified individual look at the area, in person - to OK it for the work planned.