Born in
Turin,
Piedmont, Giuseppe followed the footsteps of his elder brother
Sebastian to start his career at
Juventus, one of the two largest teams in Piedmont, as well the Italian team with the most Serie A titles. Giuseppe was a player of the
under-20 reserve team from 2008 until 2010, where he won the
2010 Torneo di Viareggio with the "bianconeri" playing as an
attacking midfielder; Giuseppe was a member of the under-18 team in the 2007–08 season, for the
Berretti reserve League. In the summer of 2010, Giuseppe left for Italian fourth division club
Carrarese in a
co-ownership deal, where he won
the promotion playoffs. In June 2011 the deal was renewed; Carrarese also signed another attacking midfielder
Luca Belcastro from Juventus during the same transfer window. Giuseppe made 16 starts and 9 substitute appearances as forward for Carrarese in the
2011–12 Lega Pro Prima Divisione. In June 2012, Juventus gave up the player's entire rights to Cararese. That window Carrarese also borrowed more players from Turin, such as forward
Francesco Margiotta. On 31 August 2012 Juventus also transferred the co-ownership of Belcastro to Carrarese; on the same day Giuseppe left for fellow third division club
Viareggio. Before he left the club, Giuseppe played twice for Carrarese in the
2012–13 Coppa Italia, scoring once in the first match, and starting as a
winger. Belcastro, Giovinco and Margiotta were the substitutes in the second match. Giuseppe was Viareggio's joint-top-scorer in the league with 7 goals, along with
Simone Magnaghi. Among the whole Group B of the third division, they were joint-16th, along with other players such as Belcastro. Giuseppe also played 4 times (4 goals and two bookings) in the
2012–13 Coppa Italia Lega Pro, in which the team finished as runners-up. He missed the return leg of the cup final due to suspension for his second booking of the tournament in the first leg. The team drew 1–1 with
Latina and was defeated on aggregate. On 5 July 2013 Giuseppe was signed by Serie B newcomers
Spezia on a free transfer; he was initially a member of the team during the club's pre-season camp, however, one month later, he joined third division club
Pisa in a definitive 2-year contract deal. In January 2015, Giovinco was acquired by Lega Pro side
Savona, signing a -year contract with the club. On 16 October he was released. In January 2016 he was signed by
Tuttocuoio. The following summer he moved to
Catanzaro. On 8 September 2019, he signed with
Ravenna. On 29 August 2020, he joined
Renate. On 20 August 2021, he joined
Taranto. In August 2022, Giovinco signed for refounded
Serie D club
Catania. On 1 September 2023, Giovinco signed for Serie C club
Virtus Francavilla. On 1 February 2024, he was loaned by
Fermana. On 22 August 2024, Giovinco joined
Taranto for one season. ==Style of play==