"No comfort or ease. I'm begging you please, God bless the deceased," she laments in the song.
Praising her mother's "beauty and intelligence", the song says that the "whole world is weeping" over the murder.
"Shot in the back of your ear, so young in 54th year, murdered with three kids left behind, a hopeless nation without you, you are in all their hearts," it says.
The teenager, a student at Edinburgh University, then repeats the chorus line "I would take the pain away".
A video to accompany the song shows footage and photographs of her smiling mother while election campaigning shortly before her death in Rawalpindi in December 2007 and of public grieving after her death.
Ms Bhutto was killed in a gun and bomb attack on her convoy - blamed on Islamic militants - as it travelled through the city's Liaquat Bagh park. She had just finished addressing an election rally.
Information Minister Sherry Rehman - who for several years was an aide to Ms Bhutto - told the Reuters news agency that Bakhtawar wrote the lyrics and music while studying in Edinburgh.
"It's a tribute of a grieving daughter to her iconic and loving mother," she said.
Ms Rehman said that while music was a hobby for Bakhtawar, she had no plan to pursue it as a career.
The song has had mixed reviews in the British press.
"While her dirge-like rap is unlikely to secure her a Grammy, the seemingly heartfelt tribute might win her some fans," The Independent newspaper says.
The Guardian says that she uses the song to "pour out her anguish".
Ms Bhutto's widower and Bakhtawar's father, Asif Ali Zardari, became president of Pakistan in September.
Their son, Bilawal, 20, studies at Oxford University in the UK and another daughter, Aseefa, 14, also studies abroad.
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