Few records released this spring will feature a dead dog’s bones as percussion, and what sounds like a simulated sex act between a singer and a piano. But then, few recording artists are quite like Fiona Apple, a performer whose relatively slim body of work – this is her fifth full-length record – belies her years toiling in the dark heart of the music industry (coming up to 25).

Fetch the Bolt Cutters is a strange and exceptional record, even within the context of an uncommon career. It shakes, rattles and rolls with unorthodox percussion, and on the opening track – I Want You to Love Me – the singer hiccups in ecstasy, facing off against an arpeggiating piano as though competing to climax first.

Although veteran engineer/producer Tchad Blake had some input, and Apple sought the assistance of her drummer’s father, sound engineer John Would, Fetch the Bolt Cutters marks the first time she has entirely overseen production on one of her albums. Knowing her own mind is a major theme. “I would beg to disagree, but begging disagrees with me,” she swaggers on Under the Table, a wickedly funny song about how she is a nightmare date at pompous dinner parties. (“Kick me under the table all you want.”)

Freedom is another overarching concern: a New Yorker article revealed that LP’s title is lifted from the TV series The Fall, when Gillian Anderson’s detective protagonist utters the phrase before entering a room where a girl had been tortured.

Most of Fetch the Bolt Cutters was recorded by Apple at home using a variety of percussion solutions as well as more conventional piano, guitar, bass and drums. Her band often workshopped the clatter, “playing” seed pods and surfaces. The result is a record that is whimsical and hardcore at the same time, one that recalls Joni Mitchell’s The Jungle Line and Tom Waits’s Bone Machine, and, intermittently, Beyoncé’s latterday, African-inspired work.

Apple’s already elastic voice ranges from fritillary flutter to guttural howl on these 13 songs; it is sometimes multitracked as she skewers antagonists, rolls her eyes at her boyfriend’s collection of guitars and ponders the aftermath of relationships. Apple is especially keen to hijack the rhythms of work songs and playground chants. In contrast to her previous celebrated works, with their Jon Brion string arrangements, Benmont Tench keys and debt to jazzy piano bars, Fetch the Bolt Cutters is raw and free-form, but no less cogent or mesmerising. Privileging rhythm is not new to Apple – see Hot Knife, from her 2012 album, The Idler Wheel. But nothing in her previous work foregrounds textures quite like these metallic scrapes, which seem to echo the title’s falling chains. The insistence of the rhythms gives free voice to the OCD with which Apple has previously struggled.

The late 90s were not a great place to be a highly strung 17-year-old prodigy, catapulted to fame with an album that mixed chamber pop with hip-hop beats. Apple’s sung cadences still often track the flows of rap. She was marketed as both sexually free and damaged, a legacy that leaves the mature Apple with plenty of wider import to chew over, as well as her own granular personal concerns. The abuse of women is one of her themes. Here, For Her contains one of Apple’s most eyebrow-raising lyrics. “Good morning, good morning/ You raped me in the same bed your daughter was born in,” she snarls. The track was written in the aftermath of the accounts of sexual assault given to the US senate judiciary committee, which failed to block the confirmation of Brett Kavanaugh to the supreme court.

There is a lot of looking back on Fetch the Bolt Cutters. Shameka recalls Apple as a kid, dodging bullies on the walk to school, finding rhythms in dry leaves and latching on to the encouragement of mentors. The younger Apple’s output was always preternaturally wise, but Fetch the Bolt Cutters seeks to unlearn the studio gloss of her previous albums while making full use of all her experiences.

If the grain of this album is purposely rougher-hewn, with boxy acoustics trading off with the odd sub-bass boom, the songwriting remains complex and elevated. Songs such as Ladies convene an audience of women – future and former partners of her own partners – Apple wants to befriend, but cannot.

Relay, meanwhile, swaps between a cheerleading chant and R&B. It’s a spectacularly acerbic song about refusing to indulge in the game of acrimony. “And I see that you keep tryna bait me,” pouts Apple, “and I’d love to get up in your face/ But I know if I hate you for hating me/ I will have entered the endless race.”

The title track rues the mistakes Apple made as a younger woman, and bridles at those who controlled her. She invokes Kate Bush, another artist who became famous very young and quickly outgrew the confines of pop.

“I grew up in the shoes they told me I could fill,” Apple sings, “Shoes that were not made for running up that hill/ And I need to run up that hill/ I will, I will, I will.” If this engrossing album opens with one kind of breathless climax, Fetch the Bolt Cutters ends with Apple panting, having finally crested the summit.

• This article was amended on 19 April 2020. It previously said that Fetch the Bolt Cutters was Apple’s fourth album: it is her fifth. A misspelling of the name of one the tracks, Shameika, has also been corrected.