George Cleghorn was born in Calcutta, Bengal, India, on 1 September 1850, the son of Susan Price and her husband, James Cleghorn, a harbour pilot. He received his medical training at St Thomas's Hospital, London, and qualified LSA and MRCS in 1872. He later gained the degree of MD from the University of Durham in 1891. After a period as a house surgeon at St Thomas's he emigrated to New Zealand, arriving at Auckland in March 1876 on the Brodick Castle.
Shortly after his arrival Cleghorn began general practice at Blenheim, where he was appointed medical officer to the newly established Wairau Hospital in July 1878. He quickly became known as an efficient, bold and innovative surgeon, who attracted patients from throughout New Zealand. He is said to have had one of the largest practices in the country, and became well known for his kindness and readiness to treat patients who were unable to pay. Cleghorn performed what is believed to have been the first successful appendicectomy in the country. In 1893, when the premier, John Ballance, was mortally ill, Cleghorn was called in at a late stage to operate, assisted by four other doctors, and was able to give Ballance relief from pain for the last few days of his life. When he published this case in the New Zealand Medical Journal he was criticised for breaching confidentiality by including the patient's name.
George Cleghorn was a pioneer of neurosurgery in New Zealand, and experimented with the immunological treatment of cancer as advocated in America by W. B. Coley. He also became an enthusiast for the work of Alexander Haig of London on uric acid in the body as a cause of disease. When the New Zealand branch of the British Medical Association held its first annual meeting in Nelson on 9 March 1897, Cleghorn was elected president for a one-year term.
George Cleghorn was married three times. On 8 September 1877, at Picton, he married Harriet Louisa Mossop. They had two children, both of whom died in infancy; Harriet died in 1881. Five years later, at Blenheim on 6 April 1886, Cleghorn married Annie Browning. She died a year later after giving birth to a daughter. On 6 July 1888, again at Blenheim, George Cleghorn married Annie's sister, Helen Browning. They had two children.
In 1900 Cleghorn gave up his practice in Blenheim because he was ill with chronic kidney disease and high blood pressure. Before leaving on a trip to England he was presented with an illuminated address by the people of Blenheim. In England he undertook further medical study, and when he returned to New Zealand began a consultant surgical practice in Wanganui in 1901. He hoped to preserve his health by avoiding the demands of general practice, but died at Wanganui from a brain haemorrhage on 11 June 1902. He was survived by his third wife, Helen Cleghorn, and three children. A memorial band rotunda was erected in Blenheim by public subscription in 1903.