Axelsson was the youngest daughter of the master gardener Karl Edvin Axelsson and Mignon Axelsson. She went to school in her home town of Gothenburg and then she continued at the University of Stockholm where she took a graduate degree in teaching and journalism.
She spent the whole of 1960 in Chile, and developed a relationship with the Chilean poet Nicanor Parra. While living in Santiago she also formed a close friendship with Nobel Prize–winning poet Pablo Neruda. The events of her time in Chile and her personal experience of them are portrayed in The cradle of fire (Eldens vagga).
Later she wrote Stones in the mouth (Stenar i munnen), published under the pseudonym Jan Olov Hedlund, describing the terror and repression of Greece under the military junta. and Honey wolves (Honungsvargar).
Axelsson translated into Swedish a remarkable number of authors, among them: Pablo Neruda, Federico García Lorca, Jorge Luis Borges, Harold Pinter, Yiannis Ritsos, Octavio Paz, Sergio Badilla Castillo and Juan Cameron.
The author's trilogy which began with A dreamed life (Drömmen om ett liv, 1978), and finished with The night season (Nattens arstid, 1989) was bestowed with numerous awards, from places such as the Swedish Academy as well as from several international cultural institutions.