Repair or Replace Cut Floor Joist
You really need an engineer to give you an answer and sign off on this.  But, being this is the internet, here's my $0.02 anyway.

Your best bet is to replace the whole joist if feasible and not to disruptive to the rest of the structure.  But it will be very disruptive to the rest of the structure &amp; flooring and probably impossible to get it into those foundation pockets on both sides.  So...

I would cut the existing joist back to the middle of that knee wall or 2x4 nearest the foundation wall.  Not counting on that structurally, but you need to square off the end of the existing joist and it makes a convenient place to put the end of the new joist while you tie things together. Take off that little bit of 2x4 back near the drain pipe.

Then I would slide a new piece of joist into the pocket in the foundation wall and flush with the end of the existing joist on top of that 2x4.

Then I would sister the joist on both sides with 2x dimensional lumber of the same height as the existing joist from the foundation wall pocket back to at least 2' to 3' past the end of that huge notch.  Be generous with construction adhesive, then clamp the whole thing up and put a few bolts through to pull it together and nail it along the length.