A Lookout Might Save Your Life
You'll be a lot safer if you have a trusted assistant standing a few feet behind you watching the top of the tree for falling branches and letting you know when the tree starts to fall. Have your assistant tap you on the shoulder with a stick to alert you when it's time to vacate the area. If it's early in the cut and you get the tap, leave the saw and walk away immediately. That means a branch is falling. Near the end of the cut, a tap means the tree is beginning its descent.
Start Cutting Branches at the Trunk
Cut off branches starting at the lower end of the trunk and working to the top. Whenever possible, stand on the uphill side of the tree. Work from the left side of the trunk (as you face toward the top of the tree). This allows the safest and most efficient use of the chain saw because you can rest the side or bottom of the saw on the trunk and slice off the branches with a pivoting motion.