On a freezing night in February 1967, connoisseurs of advanced music thronged to a small concert hall beneath the Wurlitzer Building in New York to hear – also, assuredly, to get an eyeful of – the cellist Charlotte Moorman. Among them were half-a-dozen conspicuous squares whom everybody pegged immediately as plainclothes policemen. The audience, and the cops, probably knew what to expect from Moorman’s rendition of Opera Sextronique: a new composition by her frequent collaborator, Korean artist Nam June Paik. Moorman took the stage wearing an electrified, flashing bikini. She played her cello with a violin in place of a bow, and then a bunch of flowers. The bikini came off and Paik affixed a pair of twirling toy propellers to the cellist’s nipples. It was only when she neared the third aria – to be executed in football helmet and jersey, but nothing below – that the police rushed the stage and bundled Moorman through the snow to a night in the cells and a charge of indecent exposure.

Moorman had already performed topless or naked in Europe, to little fuss. Photographs from Germany and Scandinavia show audiences of bourgeois concertgoers and adepts of the New Music: all relaxed, nobody agog let alone enraged, while she played works by Satie or Paik’s more antic inventions. By the mid-1960s she was well established in New York as an interpreter of John Cage, and as the energetic if unreliable organiser of a festival of experimental art and music. She’d performed her friend Yoko Ono’s famous Cut Piece, in which the audience was invited to scissor off her clothing, or as much as they dared. But with her arrest Moorman broached the mainstream. The case made her name, but arguably unmade her in the eyes of the avant-garde. She became a chat-show staple, a novelty act. Her brief, dazzling fame, her extravagance, temerity and wit – these, absurdly, are the main reasons you may not have heard of Charlotte Moorman.

By most accounts in Joan Ruthfuss’s engaging and detailed biography, Moorman was quite the charmer – maddeningly so. At home in Little Rock, Arkansas, she escaped a miserable family – dead father, drunk mother – to become a local beauty queen, but that was never going to be enough. From a snapshot of Miss City Beautiful 1952, you can guess she already viewed her lavish beauty with casual, amused detachment. Contemporaries with whom she studied music recall her as gorgeous and chaotic, given to noisy trysts in the room above the principal’s office. Or else as a garrulous nerd, “a bit of a grind”, too ardent and intense for the state-symphony circuit, not quite skilled enough at her instrument for a classical career. Ruthfuss argues persuasively that Moorman often didn’t know what to do with her energy; she was “helpless before her own irrepressible on-stage self”.

An ‘improbable life’ … Charlotte Moorman playing an ice cello in 1976. Photograph: Kaldor Public Art Project

All of these urges and accomplishments meant she badly needed New York in the 1960s. After failing to establish herself as a soloist, and earning a reputation for lateness that she could only partly counter with her Southern graces, Moorman fell in with the avant garde. The rigour and delight with which she embraced the work of composers such as Cage, Paik and La Monte Young was matched only by the awe and indulgence with which she was treated – for a time. Though Moorman was a tireless campaigner on behalf of the new music and musicians, the mostly male experimentalists quickly tired of what they viewed as indulgence, or outright narcissism, on stage. Yoko Ono aside, the Fluxus artists blanked her. Even Cage, who had been quite willing to fool about on game shows in the 1950s, balked at the extra-musical elements she smuggled into his already bustling composition 26’ 1.1499” for a String Player. She kept adding things: a foghorn, belching, a pistol shot and a second world war bomb for a cello. Jasper Johns rolled his eyes and wrote to Cage: “C. Moorman should be kept off the stage.”

Paik, however, stuck by her. Though they were probably never lovers, they developed an intellectual and onstage intimacy that looked forward to later performance art and anticipated all manner of countercultural happenings towards the end of the decade. Moorman’s body became a prop, or maybe a parallel medium, for Paik’s video art; she wore his TV Bra and played his TV Cello: cathode-ray sculptures that blurred the boundary between body and machine in the name of Paik’s fanciful but prescient notion of “tele-fucking”. In the 1970s their partnership waned, and Moorman performed increasingly stunt-like works by composer Jim McWilliams. They made cellos out of ice, which she played till they melted. Moorman and her instrument dangled from helium balloons outside the Sydney Opera House. Cellist and cello were strung aloft on trapezes at Shea Stadium, and as they swung towards each other she managed one resonant kick in its direction. By now her avant-garde festival was a regular fixture in New York, and Moorman was dodging unpaid bills and lawsuits, working her charm on mayors and funding bodies.

An “improbable” life is right, and Rothfuss recounts it well, relying on interviews and the vast archive Moorman left when she died in 1991. The other principals in her story – Cage, Paik and Moorman’s husband – are all dead, and at times Topless Cellist feels overweighted with archival detail, threatening to turn into an inventory of who performed what, when and where. But the truth is nobody else has done this scholarship, and so Ruthfuss’s is an essential volume: not just a record of a remarkable span and its rich artistic milieu, but testament also to the ways Moorman could be so easily written out of the history of the avant-garde. A few derivative sculptures and much film aside, she was mostly a conduit for the work of others – a glorious and heroically funny presence, especially, in Paik’s art. She did not connect her career to the feminist art of her era, so it is up to contemporaries such as Carolee Schneemann and Ono (who provides a foreword) to try to restate how much she inspired and infuriated.

Her final years were dismal and exemplary in equal measure. Diagnosed with breast cancer in 1979, she decreed that her illness was work, or rather a work – “a piece of sorts”. A year later, when the cancer had spread, she threw a rooftop party and performed Cut Piece for her friends. Ono and Paik, among many others, kept her afloat over the next decade, while the cancer got in her bones. Shortly before she died, she insisted on performing with Paik’s TV Cello at a gallery show devoted to her career. She plucked and sawed at her glowing instrument, told stories and joked while some friends left the room, unable to bear her decline or her daring. But Moorman simply wouldn’t give up what she called “the elegance, the drama, the seriousness of the whole thing”.

• Brian Dillon’s Objects in This Mirror: Essays is published by Sternberg Press.