The town is home to the Ralph Stanley Museum. Ralph Stanley is a native of Dickenson County
Although originally called Holly Creek after a small stream that runs through the town, it was later named Clintwood after Major Henry Clinton Wood, a Confederate officer in the 37th Virginia Infantry.
As of the census of 2000, there were 1,549 people, 672 households, and 426 families residing in the town. The population density was 812.0 people per square mile (313.1/km²). There were 756 housing units at an average density of 396.3/sq mi (152.8/km²). The racial makeup of the town was 98.52% White, 0.19% African American, 0.19% Native American, 0.13% Asian,and 0.97% from two or more races. Hispanic or Latino of any race were 0.52% of the population.
There were 672 households out of which 21.9% had children under the age of 18 living with them, 44.8% were married couples living together, 15.5% had a female householder with no husband present, and 36.5% were non-families. 33.8% of all households were made up of individuals and 17.7% had someone living alone who was 65 years of age or older. The average household size was 2.10 and the average family size was 2.65.
In the town the population was spread out with 16.5% under the age of 18, 8.3% from 18 to 24, 23.2% from 25 to 44, 27.8% from 45 to 64, and 24.3% who were 65 years of age or older. The median age was 46 years. For every 100 females there were 84.4 males. For every 100 females age 18 and over, there were 81.5 males.
The median income for a household in the town was $22,663, and the median income for a family was $30,833. Males had a median income of $29,844 versus $21,250 for females. The per capita income for the town was $16,323. About 16.0% of families and 21.6% of the population were below the poverty line, including 30.5% of those under age 18 and 16.7% of those age 65 or over.