Ignoring the cut out damage for now, I'd look at the water/termite damage first and figure out what structural part needs repairs. The sill can be cut in pieces to remove but does not have to be replaced as long piece. In fact, I'm not sure if the sill in your drawing is a sill I know. Are your joists sitting on the foundation or on the sill? A notched joist like that will crack along the cut corner. The rim joist is not a rim anymore after the addition. If the addition is attached to the rim, you just have to see if the supporting structure is still good. You may be looking at tearing out lot more than necessary to make it look like the original, but it may be a work that is not needed. 3/4" spade bit will tell you a lot about the condition of the lumber.