Kuptana was born in a settlement near the former Distant Early Warning Line station at Cape Parry, Northwest Territories, Canada and later moved with his family to nearby Paulatuk. He began his career by helping cousins Francis and Abraham Anghik Ruben to sand and polish their carvings, later working with sculptor and painter Bill Nasogaluak and as an apprentice to David Ruben Piqtoukun, older brother of Abraham and Francis. He has produced his own work since leaving the apprenticeship in 1992, and now resides in Toronto. He is brother to carver Robert Kuptana.
Floyd Kuptana's sculptures of soapstone and other stone often feature shapes of both animal and human. Frequent imagery of transformation may be considered grotesque and include works of Sedna the Inuit goddess of the sea and marine animals. His work relates both to the Inuit shamanic beliefs and his own experiences.
After coming in contact in the late 2000s with Gallery Arcturus, a public art museum and education centre in Toronto, Kuptana began working with paint, depicting animals in bright colours on found materials such as wood and later on art board and canvas. Some of Kuptana's pieces enter the market via commercial galleries including a leading source of First Nations artwork in Toronto, Bay of Spirits. Most have been sold by the artist himself for private collections in Canada, the United States and other countries.
Several works by Kuptana are in the permanent collection of Toronto contemporary art museum Gallery Arcturus. In 2018, an exhibit space on the gallery's second floor was created to showcase the artist's work in various media, as well as pieces created in collaboration with other artists.