Knowing the life cycle is helpful in attempting control. Adult sawflies emerge from decaying wood in May or June. Using a piercing organ called an ovipositor, the females lay eggs inside the leaf tissue of certain dogwoods. After hatching, the larvae go through three phases, all of which are spent living on and dining on the dogwood leaves. In succession, the larvae appear translucent yellow, then covered with chalky white material, and finally yellow with a black head and spots, about an inch long.
On my pagoda dogwood, I noticed the rapidly disappearing leaves in July and found scads of the larvae on remaining leaves, all coiled in a bunch. This is your assignment: Check your red-twig dogwood daily for the next several weeks. As soon as you see leaves being eaten, kill the larvae by squeezing them with your fingers or spray with horticultural oil or insecticidal soap, both of which smother the larvae and are far more benign than insecticides. Given the tenacity of the sawfly larvae, I'd opt for horticultural oil.
If you don't kill them, they will mature, stop feeding (hey, the leaves are gone anyway!), drop to the ground, and find decaying wood to burrow into for the next nine months or so. Therein lies your other assignment: Remove decaying wood, such as logs, near your plant; replace any rotting wood that's part of a shed or other nearby structure.
There is slightly good news: Since the foliar feeding takes place well into the growing season, the plant typically survives with minimal ill effects. Yes, it looks all eaten up, but it will fully leaf out the next spring.
Gray dogwood (Cornus racemosa), C. sericea (one of several red-twig dogwoods), and pagoda dogwood (C. alternifolia) are the most susceptible plants. Flowering dogwood (C. florida) appears unaffected.