The 2020 census found 755 people in the township.

Batesville, the smallest village in Noble County, is located in central Beaver Township.

Statewide, other Beaver Townships are located in Mahoning and Pike Counties, plus a Beavercreek Township in Greene County.

[4] The township is governed by a three-member board of trustees, who are elected in November of odd-numbered years to a four-year term beginning on the following January 1.

There is also an elected township fiscal officer,[5] who serves a four-year term beginning on April 1 of the year after the election, which is held in November of the year before the presidential election.