cutting off the side branches of a felled tree.
limbing (Wikipedia)
Limbing or delimbing is the process of removing branches from a standing or fallen tree trunk.
In logging, limbing follows felling. Limbing plays a role in fire prevention by removing branches from live trees that can otherwise serve as part of a fuel ladder allowing a fire to climb from the ground into the tree canopy. A California fire prevention guide recommends to "Remove all tree branches at least 6 feet [1.8 meters] from the ground" and "Allow extra vertical space between shrubs and trees."
In British English, limbing can be synonymous with snedding. Alternatively, limbing can be used to describe the operation on larger branches, and snedding on smaller.