How to replace a rotten wood sill plate on top of the foundation?

Professional Help is the only way to go with a job like this...

Please - get a contractor. There is a reason your house is build the way it is. Do Not try to jack up an outside, load bearing wall!

Jan is really right, a professional going to have the tools and skills to do the job right without doing any more damage then necessary! But if they do mess up, their insurance and/of bond will pay for the damage! If you make sure you hire a licensed bonded and insured contractor anyway! Don’t take short cuts and hire a handyman with no license. That’s a nightmare just waiting to happen!

Not a DIY project! Call for help.

Rather than jacking up, use house jacks to support and dig down. Jacking up a house requires that all sides of the house be jacked otherwise walls shift and drywall breaks it's taped seams.

You need to dig down rather than jacking up the house which is pretty serious business. Once you have removed all of the outside earth you should be able to do what is required. If not, a professional will resolve the issue for you. Once the area is open you will be able to get better costing. Do not do any digging if you are expecting heavy rains.

HOLY CR*P! This is not a DIY! You would need several 20 ton pump jacks under the floor joists. A crew to do the raising at each jack in small increments until the sill plate is cleared. Any deviation can crack walls, knock the walls out of square, and even collapse the wall. You need professionals for this kind of work.

I once helped a skilled carpenter level a house. It was a cabin on stilts, so we were able to go underneath the building. It was fascinating and I learned a lot - but I'm never going to do that myself. And this was relatively easy - small building, already above ground. Also what William said - small increments etc.