Put on a pair of leather work gloves to protect your hands from injury when working with a shovel.
Dig down to the point where you encounter roots in the ground. Remove as much dirt from around the roots as possible.
Sharpen the edge of the shovel with a metal file. Creating a sharp edge on the shovel will help cut through the roots.
Hold the shovel handle firmly with both hands. Raise and lower the shovel so the sharp shovel edge strikes the root at a right angle. Raise the shovel and repeat.
Place the cutting edge of the shovel on the root. Place one foot on the shovel while keeping your opposite foot planted firmly on the ground for support. Push down on the shovel with your foot to help cut through the root.