Projetto was born on 30 May 1902 in La Maddalena, Sardinia, Italy. Her father’s name was Cicillo, and she had four siblings. She married Giuseppe Frau and the couple had three children in total. In around 1946, Giuseppina moved to Florence in mainland Italy, where she lived with one of her daughters, Julia, until her death.
Projetto became the oldest living Italian-born person following the death of Emma Morano on 15 April 2017, the oldest person living in Italy following the death of Marie-Josephine Gaudette on 13 July 2017, and the oldest living person in Europe following the death of Ana Vela-Rubio on 15 December 2017. On 30 May 2018, Projetto celebrated her 116th birthday, making her the second Italian to reach this age.
Projetto died on 6 July 2018 at the age of 116 years, 37 days.