How do I repair or replace a drain pipe that goes under our cement foundation?

The damaged portion is about 3 feet straight down at the 90 degree joint on the back of our house on our kitchen sink drain. The line then continues to run under the house connecting the main line somewhere along the way. Roto Rooter's clean out went straight into the dirt and never made the turn and then came back out full of sand and spoiled/stagnet gray/black water. Is it possible to dig down and slightly under the foundation for this type of repair? Thanks so much.