Henry Widenham Maunsell was born on 22 February 1845 in Dublin, Ireland, the son of Charles Maunsell, a solicitor, and his wife, Maria. He was educated at Trinity College, Dublin, where he gained a silver medal for experimental and natural science, and graduated AB and MB in 1867. The same year he qualified LMI and gained his MRCS. He then emigrated to Melbourne, Australia, with his family. In 1868–69 he was resident surgeon at Melbourne Hospital, and there assisted William Gillbee with the first application in Victoria of the antiseptic principles advocated by Joseph Lister in Glasgow in 1867.
In late 1869 Maunsell came to New Zealand, having been appointed surgeon superintendent of Hokitika Hospital and medical officer of the lunatic asylum. He resigned from the former position after only one or two years to concentrate on his growing private practice. On 27 April 1871, at Hokitika, he married Mary Augusta Fosbery.
There is no record of the surgery Maunsell performed in Hokitika, but it is likely that he would have continued to practise antisepsis, thus keeping Hokitika Hospital at the forefront of New Zealand surgery. His predecessor, John Rutherford Ryley, had already been using Lister's antiseptic methods. In 1873 Maunsell was appointed coroner for the town. Two years later, after suffering a serious chest injury in a fall from his horse, he returned with his family to Ireland, where he took the degree of doctor of medicine at the University of Dublin in 1876. The Maunsells were returning to New Zealand on the Queen Bee in August 1877 when it was wrecked off Farewell Spit. All the passengers were rescued.
Maunsell then settled in Dunedin, where he was honorary surgeon to Dunedin Hospital from 1877 to 1891, health officer to the Dunedin City Council from 1881 to 1883 and lecturer in surgery at the University of Otago Medical School from 1889 to 1891. In 1886 he was a delegate at the foundation meeting of the New Zealand Medical Association in Dunedin, where he represented Auckland doctors who were unable to attend. His contribution in each of those positions was outstanding. He was a brilliant surgeon, possessed of considerable flair, and his operations were carried out with great technical skill, originality and boldness. In surgery of the abdomen and the brain he was well ahead of his time. He was a New Zealand pioneer in cleft-palate repair and also had a most fertile brain for devising new surgical procedures. While he was in Dunedin he introduced a new type of hernia operation, a new method for removing the tongue and one for excision of the rectum. In each case the technique was simple and novel. His method for stitching the bowel was based on the way he saw his wife sew the lining in a sleeve by first turning it inside out. This method was considered by many of the leading British abdominal surgeons of the day to be the best then available for bowel suture. In February 1889 in Dunedin, Maunsell successfully removed a hydatid cyst of the brain through the hinder part of the skull, in what was probably the world's first brain operation by that approach.
Although absent-minded, Maunsell was said to have been a charming companion, and he was always ready to assist and advise colleagues. He was an outstanding teacher, beloved by his students and exercising almost hypnotic powers over his classes. He was also a competent artist and his lectures were illustrated with his own drawings.
In 1891 Maunsell took leave and visited the leading European centres of surgical teaching. While in Britain he resigned from his Dunedin positions and commenced a consultant surgical practice in South Kensington, London, in 1893. He died in London on 21 February 1895, from bronchitis following influenza (which was then epidemic). He was survived by his wife and three daughters.