Cimarron is located at 37°48'30N, 100°20'51W (37.808332, -100.347413). According to the United States Census Bureau, the city has a total area of 2.4 km² (0.9 mi²), all land.
As of the census of 2000, there were 1,934 people, 720 households, and 526 families residing in the city. The population density was 820.6/km² (2,119.9/mi²). There were 749 housing units at an average density of 317.8/km² (821.0/mi²). The racial makeup of the city was 92.50% White, 0.41% African American, 0.62% Native American, 0.16% Asian, 0.10% Pacific Islander, 4.86% from other races, and 1.34% from two or more races. Hispanic or Latino of any race were 9.82% of the population.
There were 720 households out of which 39.6% had children under the age of 18 living with them, 60.7% were married couples living together, 8.9% had a female householder with no husband present, and 26.9% were non-families. 24.3% of all households were made up of individuals and 11.1% had someone living alone who was 65 years of age or older. The average household size was 2.65 and the average family size was 3.17.
In the city the population was spread out with 30.6% under the age of 18, 8.3% from 18 to 24, 28.0% from 25 to 44, 21.7% from 45 to 64, and 11.4% who were 65 years of age or older. The median age was 34 years. For every 100 females there were 96.5 males. For every 100 females age 18 and over, there were 94.8 males.
The median income for a household in the city was $41,379, and the median income for a family was $48,636. Males had a median income of $31,402 versus $21,406 for females. The per capita income for the city was $17,970. About 4.6% of families and 6.9% of the population were below the poverty line, including 8.1% of those under age 18 and 9.5% of those age 65 or over.