As a Croat from Bosnia-Herzegovina, during World War II he was a member of the ZAVNOBiH and was later appointed as a minister in the first government of People's Republic of Bosnia and Herzegovina from 1945 to 1946.

[7] He was close to the Catholic Church and his practice was also employed as a legal representative for Herzegovina Franciscan friars’ in Kingdom of Yugoslavia.

[11] During the German and Italian invasion of Yugoslavia in April 1941, Spužević and his friend fra Leo Petrović organised negotiations between the surrendering Yugoslav army and invading Axis forces, still fighting in the Mostar area.

Soon, ustaša campaign of ethnic cleansing, directed against Serb, Jewish and Roma population (as well as all Croat opponents and dissidents) reached Mostar.

In July 1942, according to his diary, Spužević tried to intervene with the ustaša minister of the interior Artuković to save some Mostar families, including Serbs, from the internment or execution.

Prominent pre-war members of the ustaša-banned Croatian Peasant Party were also targeted, for instance dr. Ivica Milaković and Blaž Slišković (killed in Jasenovac Concentration camp).

Spužević was saved by an intervention of fra Leo Petrović, a prominent Franciscan friar well respected among the population and recognized as such by ustaša authorities.

[22] In front of Dalmatian and Herzegovinian partisan troops parading in Mostar, he decried those still not joining the National liberation army in their fight against the Axis, choosing instead to wait together with the fraction of pre-war Croatian Peasant Party and its chairman Vladko Maček.

On the other hand, after the breakup of Socialist Yugoslavia, a street in western part of Mostar was named after his cousin, Đuro (Đuka) Spužević, who was entrusted by ustaše regime with a position of a Hum county prefect during the war.

Serb orthodox priest in Mostar, Radivoje Krulj, stated he was "thrilled" to have learned of the action and that Spužević's name reminds him of compassion and thankfulness.

[22] Dr. Cvitan Spužević, poznati rodoljub i ugledni Hrvat Hercegovine, duboko ganut rijetkim slavljem koje je Mostar doživio, u svome govoru naročito je podvukao zahvalnost koju narodi Hercegovine duguju oslobodiocima Mostara, a zatim oštro napao i osudio protivnarodni rad hrvatskih reakcionara koji se kupe oko izdajnika Mačeka.