Born at Oswaldtwisle in 1832, he moved at the age of 10 to Pendleton, where he became a Sunday school scholar at Bethesda MNC. Later he became Sunday school superintendent and a local preacher at Salem MNC, Salford, as well as circuit treasurer in the 1880s. In 1851 he was one of sixteen young men paid by the Manchester & Salford SSU to attend evening classes conducted by Daniel Stone, a popular lecturer on chemistry; fifty years later he was still attending classes, now at Owens College. At 21 he entered the employment the decorating business of Ward of Strangeways. In 1857, instructed to work on the Sabbath to prepare for the Manchester Arts Exhibition, he refused and insisted on taking his preaching appointments. This seems to have established his reputation with the firm's customers; he subsequently became a partner and within 12 years was the largest employer of this type of business in the town.
A Liberal in politics, he was elected a councillor in 1866, alderman in 1881, and Lord Mayor in 1884, 1887 and 1888, being knighted in the latter year. As Chairman of the Waterworks Committee he was the driving force behind the Thirlmere reservoir in the Lake District to supply Manchester with water. Although the legislation received the Royal Assent in 1879, Harwood only laid the foundation stone of the dam on 22 August 1890, a plague commemorating this event. When the construction of the Manchester Ship Canal, constructed between 1887 and 1894, ran into financial difficulties he was instrumental in rescuing the scheme by persuading the council to purchase shares in the company. He also served in 1888 on the Royal Commission for Markets and Tolls.
He was described as an 'autocrat with an overbearing manner' and in the Town Hall was 'respected and feared in pretty equal proportions'. He resigned from the council in 1905 and died on 15 April 1906.