Upon release, "Sweet but Psycho" appeared on various Spotify playlists before peaking at number one in 22 countries, including Sweden, Finland, Norway, and the United Kingdom.

An accompanying music video was directed by Shomi Patwary and depicts Max's character assaulting a man portrayed by model Prasad Romijn.

APG founder Mike Caren suggested that Max should appear on "Sweet but Psycho" to Love, which was the latter's introduction to executive production.

In a 2021 interview with Rolling Stone, Love expressed happiness in her role of Max's breakthrough using "straight pop" since "every song on the radio was rap".

[5] "Sweet but Psycho" was released for digital download and streaming by Atlantic Records as the first single from Max's debut studio album Heaven & Hell (2020).

[10][14][18] A kick-drum roll is used in the downbeat, which also includes a stereo call and response in every fourth measure of the chorus, coming second in the verse, and the first half of the pre-chorus.

[11] Chris DeVille of Stereogum compared "Sweet but Psycho" to Eurodance songs such as La Bouche's "Be My Lover", Eiffel 65's "Blue (Da Ba Dee)", and Cascada's "Everytime We Touch", along with Lady Gaga's electropop singles "Poker Face" and "Bad Romance".

[19] The lyrics of the track describe the perception of women in relationships; the word "psycho" refers to the feeling of being accepted for having an outspoken personality.

[14][20] A quotation from the American television series 30 Rock is referenced in the chorus' lyrics, "Grab a cop gun kinda crazy / She's poison but tasty".

The Dirty Disco remix fuses layered piano chords and synthesizer stabs with drum programming to make the song sound "tribal".

[12][18] Sam Brooks of The Spinoff called it "a Frankenstein of a pop track" and said the song would fit the tracklist of Lady Gaga's 2008 debut album The Fame.

[24] It topped the Swedish Spotify chart and had strong engagement in Bulgaria, which led to Caren recommending the song should be established in Nordic countries before expanding to the United States.

[28][29] Writing about the song's international performance, Dan Rys of Billboard compared it to promotional strategies used by the Backstreet Boys and Dua Lipa, stating that they "have always worked in Europe and outside of America".

[47][48] The song topped the New Zealand Singles Chart on January 7, 2019, where it was later certified platinum by Recorded Music NZ (RMNZ) for selling 30,000 units in the country.

Kheraj stated the song "boasts lyrics akin to clickbait, pejoratively using terms such as 'psycho' and 'crazy' to evoke a sentiment that seems starkly at odds with the recent progress the music industry has made in how mental health is discussed".

She defended the use of "psycho", stating the word has "a deeper meaning" and that she wanted the mental illness-related music video to be a theatrical experience for everyone.

[53] The music video for "Sweet but Psycho" was directed by Bengali American filmmaker Shomi Patwary and features model Prasad Romijn.

An ending for the music video in which Max wakes up from a dream was filmed, though the sequence was scrapped because Patwary disliked the cut and wanted it to finish with an open-ended conclusion.

Max then picks up a baseball bat, throws darts at a board with his face on the bullseye, drinks a glass of red wine, and smokes a cigarette.

Hannah Hightman of V magazine described the music video as an "aesthetic psychosis", stating Max's psycho characteristics are "too possessive, too dominant, too uninhibited".

She wore a pearl white corset and tulle skirt that covered her jet-black leather pants while the background lighting alternated between blue and red as four catsuit-wearing dancers performed a synchronized shoulder shrug.

[60] She appeared on The Ellen DeGeneres Show to perform the song on April 11, 2019, wearing a black outfit with her signature hairstyle while being joined by a group of dancers.

[64][65] She wore a green-and-purple long-sleeved outfit that was made by Zemeta, black leather pants, silver Steve Madden stiletto boots, and an iridescent Avec Les Filles trenchcoat.