To prevent a limb from peeling down the side of the tree when you are cutting it, saw part way through the branch from the underside first. Make that upward cut very close to the trunk, and about one third of the way through.
Then start cutting the limb off from the top. When you've sawed down almost to the bottom cut you've made, the limb should break away cleanly.
This is really helpful when triming small limbs from fruit trees, because the peeling bark could cause a wound on the tree allowing insects and disease to enter.
KP, WA, entered 1999-12-19