Welcome to Christianity Haven, thank you for visiting! If you have not already, we invite you to create an account and join in on the many discussions we have!
Dead branches will begin to decay. You want to cut off dead braches to live wood so that the wound can heal over by new growth. Otherwise the decaying brach can introduce decay into the good part of the tree. Also, they don't look so good if it is a landscape tree.
What do you do with a branch that has been decaying for 2000 years?
You trust God to do the pruning.
Besides trusting God, wouldn’t you also want to take some precautions, so as not to let the living part of the tree get infected with whatever diseases the dead branch might be carrying?