Yes, if it were mine, I would begin cutting down where there is the possibility of viable, healthy tissue. Be sure to clean the shears thoroughly with alcohol between each cut. Just keep cutting a couple of inches each time until you come to "clean" tissue, with no brown/black coloration. That tissue should ooze white sap. If it is not oozing, its probably not viable tissue. Plumeria don't need moister to root. I rooted my plumeria for decades in buckets of 100% coarse perlite and never watered. All I did was spritz the tiny leaves at the tip every few days. I root my plumeria in one of the greenhouses, and during the spring and summer months, it can easily get 115-120 F there. That's the only reason I spritzed with water. Just to keep the leaves and upper stem sort of hydrated.
