Uriash Puqiqnak was born in 1946. All his life, he has been surrounded by other artistic people — his one brother Louie Qingnagtug is a also a carver, the other brother Leo Hummituq is a jewelry carver and his sister Mary Porter makes wall hangings. His wife Lorraine is an artist and their son Wayne is a carver. His father-in-law was the well-known carver Nelson Takkiruq (1930-1999).
In July 2005, Uriash was appointed as a Member of the Order of Canada, in honour of his carving status.
Uriash has also been involved in politics. His political career began when he was elected mayor of Gjoa Haven. After that, he was elected to the Nunavut Legislature in the 1999 Nunavut general election. He became the MLA for the Nattilik electoral district. While he was in government, Uriash helped to develop programs that promoted home grown Inuit art and discouraged counterfeit carving from entering the marketplace. He currently serves as a member of the Nunavut Tourism Board and is chair of Parks Canada History steering committee.