Karen, the simple answer is any root you cut will be damaged. Some trees roots die when damaged, other types seal the wound and branch. However, there are many myths out there about tree roots; maybe some of this info will help.

The working roots, the fine roots which absorb all of the water and nutrients grow in the top layer of the soil. They are usually found in the top 18 inches of the soil and here in Florida where the soil is coarse textured and sandy. in the top 8 to 10 inches of the soil. Of course, the heavier, woody, scaffold roots can grow very deep.

The other myth is that the root system of a tree looks like in size and shape, the canopy. Here is an outdated incorrect borrowed image:

Over the last decade or two, research has proven what many of us who dig in the dirt already know, tree roots spread out way beyond the dripline. In fact, depending on species and soil type, tree roots can spread 1 ½ time to 5 times the width of the canopy. Here is another borrowed but correct image to illustrate:

If you must build a wall and excavate the area in the tree roots, it is best to gently expose any large roots and make clean cuts. This is like pruning the canopy, damage is done but if the procedure is worked with care, the roots will suffer minimal damage, usually.

You did not say what species of tree you are working with or what percentage of roots are going to be damaged, the general rule is that such damage should be kept to less than 30% of the total root system to prevent major damage to the tree overall.