Small wounds to the trunks are not serious but may act as entry points for fungi which cause decay later on. There may not be enough tissues left to conduct food down or water up and the tree will decline and may die. The strength of the stem may also be weakened. Broken branches should be pruned back to their main branches using the proper pruning techniques. Painting wounds or pruning scars actually increases decay organism activity, so it isn't recommended except for oaks to prevent oak wilt disease infection in May and June.
Severed roots can be the result of lowering the grade, new construction or trenching.
This type of damage has few remedies. Severing roots reduces water and nutrient uptake, eliminates stored energy and may compromise the stability of the tree. When the grade is lowered by more than two inches, vital feeder roots are eliminated, nutrient rich topsoil is removed and the remaining root system is severely wounded. If enough of the root system is destroyed or detached, the tree will die. It should also be removed because it is hazardous.