Groveton is the northern terminus of a railroad track owned by New Hampshire and Vermont Rail, where it intersects the St. Lawrence and Atlantic Railroad. This was formerly the junction of the Grand Trunk Railway and the Montreal Railroad -- a major point of access for the northern White Mountains.
The area was once known for its large corn and potato crop, starch mills, and other manufacturing (leather, shoe pegs). More recently, the town economy centered on the lumber industry. That, however, changed in 2007, when the Wausau Paper Mill closed, eliminating 300 jobs.
There are several mountains in town, including Morse Mountain (above sea level), Cape Horn Moore Mountain and Spaulding Hill (). The town's highest point is above sea level on a spur of the Pilot Range on the town's eastern boundary.
Cape Horn State Forest is located in the central portion of the town boundaries.
There were 989 households out of which 32.3% had children under the age of 18 living with them, 51.3% were married couples living together, 10.1% had a female householder with no husband present, and 32.6% were non-families. 26.7% of all households were made up of individuals and 13.5% had someone living alone who was 65 years of age or older. The average household size was 2.47 and the average family size was 2.91.
In the town the population was spread out with 26.2% under the age of 18, 6.8% from 18 to 24, 27.6% from 25 to 44, 23.5% from 45 to 64, and 15.8% who were 65 years of age or older. The median age was 38 years. For every 100 females there were 98.5 males. For every 100 females age 18 and over, there were 95.1 males.
The median income for a household in the town was $31,570, and the median income for a family was $34,444. Males had a median income of $33,281 versus $19,464 for females. The per capita income for the town was $15,101. About 9.4% of families and 11.4% of the population were below the poverty line, including 13.4% of those under age 18 and 10.1% of those age 65 or over.