Ask Mr. Smarty Plants

Cornus sericea ssp. sericea (Redosier dogwood or redtwig dogwood) is listsed as a larval host for Celastrina ladon (Spring azure).  It seems its caterpillar has at least two forms—both green and pinkish—depending on what it is feeding.

The sawfly larvae (Macremphytus tarsatus) is reportedly a significant pest on dogwood (Cornus) species.  It, too, has several forms.

Here is a list of moth caterpillars that feed on Dogwood Shrubs and here are links to photos of some these caterpillars:

White-lined Bomolocha, Euthyatira pudens,  Hyalophora cecropia, Hydrelia albifera, Hypagyrtis unipunctata, Probole amicaria, Schizura unicornis and Xanthotype sospeta.

Monarch butterflies do, generally, feed on milkweed plants, but they will also feed on other members of the Family Asclepiadaceae (Milkweed Family) such as  Matelea species, Cynanchum species and Funastrum species.  I doubt that they would feed on Cornus species in the Family Cornaceae (Dogwood Family).

Perhaps one of the caterpillars above is the one you are seeing.  Whatever the caterpillars are, if they are destroying your dogwood tree, you probably want to remove them.  It can be very effective to put on some gloves and simply pick them off and put them into a container of soapy water, vegetable oil or water with insecticidal soap.  You can also consider using a natural insecticide, Bt, that comes as a powder that can be sprinkled on the leaves or can be mixed with water and sprayed.  As with all insecticides, please read and carefully follow instructions for application and safety.