Granite Quarry was originally named Woodville when it was founded in the late 1800s. However, the first post office in the town was established under the name of Woodsides in 1891, after a prominent family in the area named Woodsides. The name was officially changed to Woodsides when the town was incorporated on March 7, 1901 by the North Carolina General Assembly. Jerry L. Shuping was the first mayor. The first town meetings were held in an upstairs room in the W. S. Brown store building. What is now the Town Hall Municipal Building was originally built in 1963 by Gemgas, and purchased later by the town.