Purves was born in Edmonton on October 18, 1933. He grew up in the city's Riverdale district and graduated high school in the city. On December 29, 1956 he married Clare Heller, with whom he would have four daughters.
He worked for the Dominion Bank from 1950 until 1959, and worked for his family's upholstering firm, Apex Auto Upholstering, from 1950 until 1988.
Purves did not graduate from university, but has taken a variety of business and self-improvement courses.
Purves' first bid for political office took place during the 1964 municipal election, when he ran unsuccessfully for Protestant school trustee. He finished eleventh of twenty-one candidates; the top seven were elected.
He ran for Edmonton City Council instead in the 1966 election, and was elected as one of twelve aldermen, finishing ninth of thirty-two candidates. He was re-elected in the 1968 election, finishing fifth out of thirty-two candidates. While still in office, he sought the Social Credit nomination in Edmonton-Strathcona for the 1971 provincial election, but was defeated by Strathcona Centre incumbent Joseph Donovan Ross (who was defeated in the general election by Progressive Conservative Julian Koziak). In the 1971 election, Edmonton was for the first time divided into aldermanic wards; three aldermen would be elected from each of the four wards. Purves ran in Ward 2, and finished first out of eleven candidates.
In the 1974 election, Purves ran for mayor, challenging incumbent Ivor Dent. He defeated Dent, but so did William Hawrelak, who received more than twice as many votes as Purves. Hawrelak died in office and was replaced by alderman Terry Cavanagh, who Purves challenged for mayor in the 1977 election. In winning, he beat not only Cavanagh (who finished third) but Dent (who finished fourth) and future mayor Laurence Decore (who finished second). Purves faced no serious opposition to his 1977 re-election bid, and won more than seventy percent of the vote.
Purves was defeated in the 1983 election by Decore, who received more than twice as many votes as the incumbent. He did not seek to re-enter politics thereafter.
Purves served as a member of the St. Joseph's Hospital board, the Edmonton Police Commission, the Greater Edmonton Foundation board, the Edmonton Chamber of Commerce, and the Edmonton Symphony Association board. He was at various times president of the Edmonton Exhibition Association, and the Edmonton Jaycees (a youth association). He was also bishop of the 7th Ward (Edmonton) of The Church of Jesus Christ of Latter-day Saints.
He filed for bankruptcy on March 29, 1988.