It is hard to consider the Cuban-American artist Ana Mendieta without viewing her through the prism of her death. Early in the morning of 8 September 1985, Mendieta fell 34 floors from the bedroom window of the Manhattan apartment that she shared with her husband Carl Andre, the Minimalist sculptor to whom she had been married for eight months. She was 36. Accused of murder, Andre was acquitted in a non-jury trial — but even so, there are still people today who believe that he was guilty. Mendieta, meanwhile, has become something of a cult figure — part victim, part heroine of feminist art.

Strange to say, not much of this terrible story is related in the Hayward Gallery’s new exhibition Ana Mendieta: Traces, the first UK retrospective of her work — a rare reference to Andre is a book of modest lithographs on which the couple collaborated. The idea is that we should focus on Mendieta’s life rather than her death. This is laudable but it runs the risk of visitors unfamiliar with the artist leaving the Hayward ignorant of the manner of her death, which, in my view, is an important aspect of her reputation.

Born in Havana, Mendieta arrived in America in the wake of the Cuban Revolution when she was 12. In the late Sixties, she studied painting at the University of Iowa, but soon gave that up in favour of performances involving her own diminutive body (she was 5ft). Photographs documenting some of these are displayed in the first room of the exhibition at the Hayward. In one gender-bending series, she attaches tufts of a friend’s black beard to her own face. In another, she presses a pane of glass against her naked breasts and buttocks, distorting the flesh into strange shapes, like parts of an unfortunate creature splattered against a windscreen.

This paved the way for the bewitching and original work of the Seventies, which fused ritual, derived from her interest in the voodoo-like Afro-Cuban religion of santeria as well as ancient Mexico, with the female form situated in the landscape. In one famous photograph, which is considered the first of around 100 distinctive “Siluetas”, or silhouettes, and was taken in an ancient Zapotec grave in Yagul in Mexico in 1973, we see her corpse-like body smothered with sprays of white flowers, like a sprinkling of fairy dust. It put me in mind of Millais’s Ophelia.

Like much of her best work from this period, which involves blood, feathers, shrouds and fire, it has a subtle and metamorphic power reminiscent of late Shakespeare, and is thick with the same promise of regeneration and a pagan sense of benign natural magic. In another photograph, we see her caked in mud and specks of greenery, camouflaged against the bark of a tree — a sylvan sprite, perhaps, or a reworking of the myth of Daphne transformed into the laurel. Mendieta wanted her work to evoke the sensation of looking at the mouldering ruins of a forgotten civilisation overgrown with grass, and it certainly has a potent, ancient quality, like half-remembered archetypes from our collective unconscious.

In the early Eighties, her art changed direction, as she began to work principally indoors. On the evidence at the Hayward, it suffered: the flat, floor-bound sculptures, made from supposedly “sacred” earth and sand, are weak, as are the drawings incised onto leathery leaves.

In her quest to create a contemporary equivalent of runes and carvings of primitive fertility goddesses, Mendieta wanted to simplify the female form in the manner of late Matisse. But her art, which lacks the refinement of the Frenchman’s joyous and elegant late cut-outs, works best when it taps into something rawer and more visceral. Moreover, her borrowings from ancient cultures occasionally feel too easy — the art equivalent of New Age types offering henna tattoos of swirling, Druidic patterns that have no real meaning.

This exhibition, then, confirms what we already knew: Mendieta’s earthbound performances of the Seventies have the strangest, densest and most compelling psychological complexity. Surely she would have returned to tap this rich vein had she lived.