After dropping out of high school, Oehlenschlæger and her sister moved to Copenhagen, starting off as a model and entrepreneur in teeth whitening products, while her sister pursued a singing and musical acting career.[6][8] On 23 February 2023, Oehlenschlæger replaced her pregnant sister in the role of Dionne for the premiere of the musical Hair at the Østre Gasværk Teater, making her debut as a non-stunt stage actress.[4][5][8]
On 25 January 2024, Saba was announced as one of the participants of Dansk Melodi Grand Prix 2024, the Danish national final for the Eurovision Song Contest 2024, with the song "Sand".[4] She went on to win the final on 17 February 2024, earning the right to represent Denmark in the upcoming contest.[9] On 29 March 2024, several entrants, including Saba, released a joint statement calling for "an immediate and lasting ceasefire" in Gaza, as well as "the safe return of all hostages".[10] Saba failed to qualify from the second semi-final on 9 May 2024, placing 12th out of 16 with 36 points.[11][12]
In 2018, Oehlenschlæger was diagnosed with bipolar I disorder and was hospitalised several times until 2020, as she explained in the 2020 DR documentary Min sindssyge tvilling (transl. 'My insane twin').[5][6][8] She also practiced self-harm during her teenage years.[8] She is an ambassador for the Danish Depression Association.[5]
Oehlenschlæger was in a same-sex relationship with Lærke-Maria Schmidt from 2020 until latest 2023.[13][14] At the Danish Melodi Grand Prix 2024, she revealed she had been in a relationship with Aviaja Larsen for 6 months.[15]