The son of popular carpero composer and instrumentalist Cayetano Saluzzi, Dino played the bandoneón since his childhood. Other than his father, he was influenced by Salta musicians such as Cuchi Leguizamón, and by the lyrical strain of the tango of Francisco de Caro and Agustin Bardi.
For much of his youth, Saluzzi lived in Buenos Aires, playing with the Radio El Mundo orchestra. He would play in orchestras for a living, while touring with smaller, sometimes jazz-oriented ensambles (including a brief stint with Gato Barbieri), developing a personal style that made him a leading bandoneonist in Argentine folklore and avant-garde music (especially since Ástor Piazzolla did not participate in projects other than his own). In the 1970s he played the bandoneón in León Gieco's megahit Sólo le pido a Dios, and made further inroads into Buenos Aires audiences by playing jazz clubs such as Music Up and popular music club La Trastienda in the Palermo Viejo district.
In 1982, he collaborated with Lito Vitale, and through word-of mouth publicity (mostly from expatriate musicians who idolized him) he was invited to several European music festivals, and landed a a contract with the prestigious ECM label. Several records resulted, including Kultrum, a 1984 free-experimental effort with the Rosamunde quartet aimed at reduced audiences.
Many ECM artists and other jazz greats have collaborated with Saluzzi. A partial list would include Charlie Haden, Charlie Mariano, Palle Danielsson, and Al Di Meola.
In 1991, Saluzzi recorded an album with his brothers Felix and Celso and his son José Mar�-a on guitar, kicking off his "family project", which has since toured many countries.
Saluzzi is known for his sometimes aggressive temper, which has led to lost opportunities. Notably, during 2004 he had a publicized row with Brazilian composer and instrumentalist Egberto Gismonti, with whom he shared many moments in the past.