Jessie Kleemann was born in Upernavik in northern Greenland and trained as a lithographic artist. From 1978 to 1979, she was a student at the Tuukkaq theatre in Fjaltring in northern Jutland, from 1984 to 1991 director of the school of arts in Nuuk, during which period she took leave in 1989 in connection with the staging of the play Asanninneq naliitsoq, based on Märta Tikkanen's Århundradets kärlekssaga. Between 1991 and 1993, she was the coordinator of the exhibition project Arts from the Arctic as part of the UNESCO programme for the decade of indigenous people. She has participated in Nordic and international exhibitions as well as in many one-person exhibitions and as a poet has represented Greenland at Nordic and international literary events. Her first independent poetry collection was Taallat. Digte. Poems, 1997.
She is especially known for her provocative performance art, in which she has developed a form of ‘body art’ based on ancient masque performances. Like the words and enactments in different performance videos, she uses the artist's body as a living canvas, often incorporating it into her exhibitions. In 1994 she provided the script for the performance Sinnattumini, based on the legend of Navaranaaq, an Inuit woman who was a servant girl with a Northmen family and became caught up in a conflict between the two peoples. The performance was a Nordic collaboration between Jessica Kleeman, Elisabeth Heilman from Sweden, and the Finnish director Ana Falenius.