For many people, cutting boards are a utilitarian item devoid of style or sentimental aspects. The only requirement is that they function properly and last for a while. But they don't have to be that way, and more people are requiring their cutting boards to not just be functional, but to be stylish as well. Making cutting boards out of a tree can be a way to create these basic kitchen necessities, even from trees in your own yard.
From the downed tree, take a chainsaw or bow saw and cut several pieces of wood around 4 inches thick. Make them by cutting completely through the trunk of the tree. When finished you should have a roughly circular slab with the heart of the tree in the center surrounded by the concentric growth rings with a perimeter of bark.
Pass the slab through a planer, setting the height of the planer to allow all but the highest part of the slab to pass through. Repeat this step as needed until the slab is flat on one side.
Turn the slab over and repeat the process until both faces are flat.
Use a random orbit sander, and sand each face using progressively smoother grits starting at 80 grit and stopping at 220.
Apply a food-safe finish to the entire board, such as mineral oil or a specialty food finish. With mineral oil you will have to periodically reapply the finish. You'll also need to coat the top and sides and wait for them to dry before coating the bottom.