This can be a real pain in the ass and in most cases you will eventually do a repair or replace the line.
I rooted mine out twice a year for about 6 years until there was enough separation that it wasn't going to do any more.
At that point a camera went down the cleanout and pointed out exact locations of separations of the clay pipe.
Mine was in the city easement and under the street for which the city wouldnt pay a dime.
I had the repair done from the curb face to the cleanout with ABS. There are products available to sleeve the inside of the pipe after rooting it, but in my research I have found that it is a temporary band-aid.
The roots could be coming from a long distance away, and are hell to deal with unless you just get in there and replace the damaged pipe.