The word “dope” derives from the Dutch word, “doop,” which means “sauce.” “Doop” is the noun form of the word, “doopen,” which means “to dip.” “Doop” was initially used in cooking contexts, but soon also came to refer to any thick, viscous fluid, such as paint, tar or beeswax. In 17th century usage, “dope” owed more to dinner than it did to drugs.
By the 1850s, “dope” came to reference medicinal preparations, including opium-based concoctions. Morphine and other narcotics fell under the “dope” umbrella at around this time, broadening its meaning to "a drug or narcotic substance."
By the early 1900s, “dope” became a slang term for any kind of illicit drug, but most often referenced heroin and marijuana, especially in jazz and beatnik circles. "Why do you think they call it dope?" emerged in the 1970s as an anti-drug message, playing on the double meaning of dope—both as a slang term for drugs and as an insult meaning a stupid person.
The answer to the question, “Why do you think they call it ‘dope’?” is saucy indeed.