The organ removal surgery is how you fix organ damage, you'll need extra organs to do so, though. Good thing is that you can survive with around 2 organs removed, so you can borrow some from your crewmates and/or buy it from places. Do note, it does not drop any organs if organ damage is above 3%, so you can't just remove it and place it back in to fix organ damage. I should've probably stated this in the description, sorry about that.