Dig around the stump with the shovel, working to get the root ball out of the ground.
Cut away the main roots with a chainsaw. Use the axe to hack through the thinner roots that anchor the cedar. Pull the roots out of the ground and dispose of them in a compost heap.
Continue to dig around the stump, working it up from underneath the root ball. Cut and remove pieces of roots until the stump and root ball are light enough to be lifted out of the ground. Dispose of the stump by burying it.
Use a stump grinder to grind the large stumps 6 to 12 inches below the surface of your lawn. Dispose of the wood chips in a compost heap.
Rent a backhoe to remove stumps that are too big for grinding with a stump grinder. Renting a backhoe is expensive but may be economical if removing multiple stumps.
Fill the craters with loam to hasten plant growth. Topsoil may be used to fill the hole as well, especially if you plan to let your lawn reclaim the space.
Gather firewood and start a fire atop the cedar stump. Keep the fire going until most of the stump has burned. Wait for the coals to cool. Remove any leftover roots with an axe and dispose of them in a compost heap.
Purchase a chemical solution that aides in the decay of wood. This can be found at the garden center of your local market. Drill holes in the stump and pour the chemical over it. It may take up to six months for the stump to decay. When the stump has decayed, remove it with an axe and chainsaw. Compost the wood only if the chemical agent you purchased is eco-friendly.
Fill the holes left by the stumps with loam. Wait for the soil to settle before planting anything in the ground once occupied by the stump.