Trees recover most rapidly from large cuts if they are smooth and do not damage the branch collar. If the branch is large, remove the bulk of it first to minimize the weight of what will fall last. First, an undercut is made, sawing to about a quarter of the way into the branch from the underside. This partial cut stops the bark tearing down the trunk if the branch accidentally breaks. Second, cut squarely from the top of the branch about 5 cm beyond the undercut (further away from the trunk) until the branch falls away - the cut should be made to the same level as the undercut. The finishing cut can the be made by following the line of the branch collar from top to bottom . Generally, the line of the cut is approximately 90 degrees to the branch bark ridge.
(above) Note first cut is an undercut and second is a top cut a little distance from the first.
(above) the same area, third and final cut must be smooth. Cut just beyond the branch collar at an equal and opposite angle to that made by the bark ridge on the main stem.
Below is a photo of a cut to remove included bark :
This is a weak point of trees and shrubs. Bark is embedded between opposing branches, creating a structurally weak point. It is best to eliminate these branches as soon as they are noted. If not, as the tree enlarges in diameter and weight, the tree is likely to split at this weak point.
In cutting much larger branches that could potentially be problematic in terms of where it will fall, a wedge can first be made to determine the direction of the fall :
Ref : RHS pruning and training manual pg. 12, 22