Ok, I think your talking a band joist and possibly the sill plate.
(You need to Login or Register to view media files and links) Yes, you want to make this repair from the outside. You can remove the band joist and the sill plate by cutting it in numerous place along the length of the damage with a circular saw and a sawzall, then using a crow bar and a pry bar to pull the pieces out.
Use your square to make square cuts on the ends where you have good wood. And you should use a Simpson plate to join the repair to the original band joist in the crawl space since you wont be able to sister it together. This isn't necessary on the sill plate.
It's possible you may need an engineers letter on this since it is structural and sounds like you are planning on selling it. If this is necessary, do this before you make the repair. He will spell out exactly what needs to be done and the connections that are required. If a contractor does this for you, expect to pay him too for making the phone call and giving the engineer the tour.
Sounds like you already have the joists and floor supported from the crawl space. You only have to jack it up enough to get the sill plate out or beat it into the crawl space with a cold chisel.
If we're talking about a single band joist, reattaching the joists is the easy part. But mark the new band joist with the joist locations before placement.
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