Beetham was born in 1840 in Horncastle, Lincolnshire, England. His father was the noted portrait painter William Beetham. The Beetham family emigrated to New Zealand in 1855, arriving on the William and Jane in 1855. Together with his brothers, he settled in the Wairarapa. The brothers built up a farm on land bought by his father, and Brancepeth Station was by 1901 the largest land holding in the Wairarapa, at 24,000 hectares (240 km2). As the land had originally been owned by Māori, Beetham engaged with them frequently and they knew him as Hori Pitama. His sister Susannah married Cecil Fitzroy in 1878.
Beetham made his first exploration of Mount Ruapehu in March 1878. In 1879, Beetham, accompanied by Joseph Prime Maxwell, a civil engineer of Wellington, made a complete ascent of Mount Ruapehu, and, reaching its summit, crossed the large southern glacier, and made a close examination of the hot lake that is in the great ice plateau, the existence of which had not been previously recorded.
Beetham represented the Wairarapa West electorate on the Wellington Provincial Council from February 1873 until the abolition of provincial government in October 1876. He represented the Wairarapa electorate in Parliament, after winning the 1877 by-election, to 1881. He then represented the Wairarapa North electorate from 1881 to 1887, and the Masterton electorate from 1887 to 1890, when he was defeated by just 18 votes. For a time, he was in Parliament at the same time as Fitzroy, his brother-in-law.
- Scholefield 1940, p. 55.
- "Brancepeth Station". Register of Historic Places. Heritage New Zealand. Retrieved 21 November 2013.
- "Marriages". Hawke's Bay Herald. Vol. XXI, no. 5016. 23 February 1878. p. 2. Retrieved 11 July 2015.
- Beetham 1926.
- Scholefield 1950, p. 237.
- Scholefield 1950, p. 95.
- "The General Election, 1890". National Library. 1891. p. 1. Retrieved 25 February 2012.
- Beetham, George (1926). The First Ascent of Mount Ruapehu, New Zealand, and, A holiday jaunt to Mounts Ruapehu, Tongariro, and Ngauruhoe. London: Harrison and Sons. Printers in Ordinary to His Majesty.
- Scholefield, Guy, ed. (1940). A Dictionary of New Zealand Biography : A–L (PDF). Vol. I. Wellington: Department of Internal Affairs. Retrieved 6 October 2013.
- Scholefield, Guy (1950) . New Zealand Parliamentary Record, 1840–1949 (3rd ed.). Wellington: Govt. Printer.