The tragically short life of this great writer makes a dramatic, seductive and difficult subject. At least a dozen versions already exist, including plays, memoirs, fictions and biographies. The fascination of the subject is obvious. There is the New Zealand family life, so furiously resented, yet so passionately invoked. There is the self-exile to England, the nomadic life, the complicated relationships with other women (the grotesquely self-sacrificing Ida Baker, for one), the edgy intimacies with writers such as Virginia Woolf and DH Lawrence, and the confused, reckless sexual experiments and mistakes.

There is the long, intense relationship with the talented, narcissistic John Middleton Murry, which disintegrated painfully. (Once, while she was very ill in Italy and he, absent, did nothing but write to her about his sufferings, she underlined all the "I"s in his letters.) There is the death of her brother in the war, and, from that moment in 1915, the amazing flowering of the writing. And there is the agonising history of her illness, culminating in the dubious Gurdjieff Institute in Fontainebleau, where she died, in 1923, at 34, still, to the last, crying out for a chance: "I want to work . . . I want a garden, a small house, grass, animals, books, pictures, music. And out of this . . . I want to be writing . . . But warm, eager, living life  to be rooted in life . . . That is what I want."

An irresistible story: but then come the difficulties. Katherine kept secrets, covered her tracks, and moved house endlessly (about 10 times in 1914, for instance), leaving papers everywhere. After her death, Murry, haunted by her all through his next two catastrophic marriages, made the most of what she left behind her. Ignoring her request that he should "tear up and burn as much as possible", he edited a stream of stories, journals and letters, all heavily altered and censored  often to reflect better on himself. In the process, which one caustic observer called "boiling Katherine's bones to make soup", he kept her writing alive. He also made a lot of money out of her, and promoted a mythologised version of a martyred Saint Katherine, "sealed in porcelain", as Anthony Alpers put it.

For Alpers and other biographers, Murry's editing of Mansfield's posthumous life was both a vital source of materials and an obstruction. It wasn't until the 1970s and 1980s that Mansfield scholars in New Zealand began to publish complete editions of her letters and notebooks. They had not only to unpick Murry's versions but to read Mansfield's handwriting; Margaret Scott told Kathleen Jones that she "once spent an entire week deciphering one word".

Her writing was as impenetrable as she was: romantic, excitable, sharp-edged, malicious and cold, charming and funny, lonely, proud, vulnerable, a wearer of masks. Her on-off friend, the artist Beatrice Hastings, is well quoted here: "A difficult person to know . . . very complex, very self-critical and self-centred, struggling to make herself different, to get rid of what she considered the bad parts of herself . . . terribly private and sometimes hard to approach."

How does Jones  an experienced biographer of an assortment of women writers  approach the challenge? She is steady, thorough, professional and unsensational. She is especially good on Mansfield's feeling for the landscape (and people) of New Zealand, on her financial situation (often desperate, and dependent on the allowance from her much maligned father), and on the frequent squalor of her and Murry's living conditions  yet another appalling furnished flat, "grimy and draughty and smelling of dust, tea leaves and match ends in the sink", yet another wretched hotel room: "I know I shall die in one. I shall stand in front of a crochet dressing-table cover, pick up a long invisible hairpin left by the last 'lady' and die with disgust."

Jones firmly sees off previous biographers, for instance on Mansfield's plagiarism of Chekhov (which Jones thinks has been over-stated), on her premature stillborn child (not a miscarriage, says Jones) and on her gonorrhea (a false diagnosis, says Jones).

There are some nice rewards for the close attention Jones pays to the sources. When Leslie, Mansfield's brother, died horribly in the war (a grenade blew up in his hand and he bled to death), all other biographies give Mansfield's version of his last words: "Lift my head, Katie, I can't breathe." Jones has noticed that in the letter Mansfield received describing his death, the words quoted were: "Lift my head, I can't breathe". Mansfield adds her name into the account. "She wants passionately to feel that her brother's last thoughts had been of her."

At times, though, these sorts of comments can sound reductive or banal. "She felt herself to be loved less than her siblings and as a result became more difficult to love." "Under her self-confident exterior, there was a much more insecure young girl." We are told that Mansfield suffers from "panic attacks" and is "good at networking". Jones is enthusiastic, but not very interesting, about the stories. And she has some blank spots. Virginia Woolf is introduced, oddly, by a passage on the conventions of the English upper classes: "Ladies do not wear makeup or perfume . . . clothes are bespoke, or purchased at exclusive shops . . . among these people Katherine is a foreigner." (Yes, Woolf could be snobbish about Mansfield, but she was not a conventional upper-class "lady".) Mansfield's brilliant, savage account of Lawrence and Frieda's marriage is solemnly paraphrased, without any sense that it might be funny as well as appalled.

The biography's main problem, though, is its structure. Because Mansfield's story is so intertwined with Murry's version of it, Jones has chosen to break the narrative into contrasting chunks of Mansfield's life and her afterlife. The Mansfield sections are told in the present tense, intercut with sections in the past tense that tell the story of Murry's next marriages and the lives of his wretched children, under the shadow of Mansfield's ghost.

To my mind, this is a disastrous decision, though other readers may find it boldly innovative. The intercutting involves awkward repetitions. The present-tense narrative has a fake-spontaneous air to it, as though pretending that everything is happening Right Now. "A dark-haired girl sits at the window gazing out at the ships moored in the harbour below her parents' house, dreaming of London." "John is completely unaware that when they make love she sometimes fakes orgasms." And so forth. Meanwhile, the past-tense sections make Murry's story too dominant (the book should have been called a joint life) and rupture the narrative annoyingly. The overall effect is of a dedicated and inexhaustible researcher who has made some unfortunate narrative choices. In fact, Kathleen Jones's relation to her subject reminded me of Ida Baker, as perceived by Mansfield: faithful, attentive, true as steel, flat-footed, and unbearably irritating.

Hermione Lee's Biography: A Very Short Introduction is published by Oxford.

 This article was amended on 18 March 2011 to remove an inaccurate statement.