There are two methods of trenchless pipe repair that won't harm your tree. One is called pipe bursting and the other is known as pipe relining.
With pipe bursting, a small access hole is made where the damaged pipe starts and ends. Then, using the broken waste pipe as a guide, a specially designed machine pulls a replacement pipe through the old pipe. This is called pipe bursting because that's exactly what happens as the new pipe is pulled through: the head of the machine splits the old pipe apart to make room for the new pipe.
The other option in trenchless pipe repair is pipe relining. With pipe relining, damaged waste pipes are left in place but lined with a fiberglass-reinforced epoxy. This creates a pipe within a pipe and the result is a super-strong new pipe that can service your home indefinitely.
Both of these trenchless pipe repair technologies are reliable and readily available from services like Roto-Rooter. Compared to the process of digging out your yard to reach the pipe, both pipe relining and pipe bursting are more expensive. However, if you have a precious tree, pool, sidewalk, driveway or other part of your landscape you'd want to protect, these trenchless pipe repair services can be very worthwhile.