I am not that Arborist but am an Arborist, CTE Certified Tree Expert, Bachelors in Plant Biology, graduate Landscape Design, licensed Pesticides, and ......
American Elms are dying from Dutch Elm disease though there are now some resistant varieties.
The dark you see is the Heartwood which is older xylem that is dead. It provides support for the tree. Its dark because of unused stored sugar, dyes, and oils. Active Xylem surrounds the heartwood and is called Sapwood. This carries the nutrients and water from the roots to the leaves. As the tree ages and becomes larger in diameter, the formerly active xylem closest to the outer heartwood dies and becomes the new heartwood.
You are not helping your tree keeping it healthier by cutting these branches like this. You are giving insects, bacteria, viruses an opening in the tree to enter. When you cut a branch, you must cut it at a bud, this is the active growth tissue. It can then heal forming a scar like seal over the wound. It should be cut fairly close to the tree. At the correct point at a branch joint, you will see rings, you want to make your cut just a hair on the last growth ring.i
Next, by cutting branches, you are reducing the number of leaves the tree has to make food for the tree through photosynthesis thus weakening the tree by starvation.
You also create sucker branches which have soft bark allowing entrance of organisms.
And, it takes a lot of energy to produce new branches, so by cutting, you are starving the tree and forcing the tree to use more of its depleting food reserves.
Trees need water and fertilizer however fertilizing a dying or a tree under stress can accelerate its decline.