Answer by  
                                                                                          LeheckaG (1826)
                                                            
                          
                          
                                                          Depends on the roots' relative size:
 
 Axe/Hatchet, hand-saw, long-pike/wrecking-bar, loppers, mattock/pick-axe, & pointed-shovel/spade
 are the normal/old-hand-tools for the job.
 
 Power (chain/circular) saws are VERY DANGEROUS to try to use on roots.
 (because of the kick-back risks)
 
 A rototiller can break up smaller roots.
 
 A (power) plough/plow, stump-cutter, or trencher is required to break up larger roots.