Roots can be cut from the drain. Fine roots are cut using what we call the screamer, if you view the video clip the reason why becomes clearer. Tougher roots can be removed using a 'Wart Hog' - an American designed head incorporating a chisel point of water combined with a damped head to prevent it spinning too quickly. In other instances it may be that a metal cutter with a spiral blade and serrated teeth is needed. This is also driven byu a high pressure water which cuts the roots and washes the resulting debris away.
Root cutting is normally carried out prior to resin lining, if the roots are just cut and no further action is taken they can continue to grow, becoming thicker and forcing the joints apart. Eventually cracking and breaking the pipe, leading to an expensive and disruptive excavation and replacement.
You may wish to view the video on resin lining.