Best time to take cuttings June thru Aug. Use 5-6 inch long terminal growth of firm new growth. apply 0.3% IBA (Rooting hormone)Stick in well drained soil & mist
takes 1year to produce a 1 gal size plant

Dogwood shrubs root quite easily from dormant branches as well. Take your 6" cuttings from last years growth, pieces about a pencils thickness.

In fact, dogwoods root very easily from layering and you may have some branches that have laid on the ground and have already rooted themselves naturally. Have a look around the base of the shrub to see if any branches have rooted where they touched the soil. In the spring, cut these branches from the "mother" shrub and dig up the new rooted branch.

I allow some of my Silverleaf and Cream Cracker dogwoods to do this every year (and even bend branches down and bury a section in the soil)and dig up many new shrubs this way.
Viburnums, Purple Smoke Bush, Blue Mist (Caryopteris) and Spireas are other shrubs I have layered to create new shrubs.

thank you so much George and Wyndyacre!!It sounds possible!