During the American Civil War, Mesilla briefly served as capital of the Confederate Territory of Arizona.
Mesilla Plaza is a National Historic Landmark.
As of the census of 2000, there were 2,180 people, 892 households, and 595 families residing in the town. The population density was 407.0 people per square mile (157.0/km²). There were 981 housing units at an average density of 183.1/sq mi (70.7/km²). The racial makeup of the town was 73.99% White, 0.23% African American, 1.01% Native American, 0.23% Asian, 0.05% Pacific Islander, 20.69% from other races, and 3.81% from two or more races. Hispanic or Latino of any race were 52.20% of the population.
There were 892 households out of which 25.6% had children under the age of 18 living with them, 53.5% were married couples living together, 9.3% had a female householder with no husband present, and 33.2% were non-families. 27.8% of all households were made up of individuals and 8.9% had someone living alone who was 65 years of age or older. The average household size was 2.44 and the average family size was 2.99.
In the town the population was spread out with 22.2% under the age of 18, 7.9% from 18 to 24, 23.4% from 25 to 44, 29.4% from 45 to 64, and 17.2% who were 65 years of age or older. The median age was 43 years. For every 100 females there were 90.9 males. For every 100 females age 18 and over, there were 90.7 males.
The median income for a household in the town was $42,275, and the median income for a family was $51,181. Males had a median income of $30,500 versus $25,000 for females. The per capita income for the town was $25,922. About 6.3% of families and 9.4% of the population were below the poverty line, including 7.4% of those under age 18 and 5.8% of those age 65 or over.