Born in Cosenza, Calabria, southern Italy, Garritano played for F.C. Internazionale Milano from Giovanissimi Nazionali under-15 team in 2008–09 season to Allievi Nazionali U17 team in 2010–11 season.
On 30 June–1 July 2011 Garritano (50% registration rights for €700,000) along with Luca Caldirola (50% registration rights for €2.5M) were left for Cesena in co-ownership deals as part of €10.5 million deal to sign Yuto Nagatomo from Cesena. Garritano signed a 3-year contract, the maximum length an under-18 player could sign. On 1 July 2011 Garritano returned to Inter on a temporary deal, for the U18 team. Garritano scored 10 league goals in the group stage. Garritano also played for Inter U19 team 8 times. After winning the league title for U18 team, Garritano was included in the U19 squad for the playoffs round of Campionato Nazionale Primavera. He played twice, in semi-finals replacing suspended Marko Livaja and again in the final as a substitute for Daniel Bessa. In June 2012 the co-ownership deal between Inter and Cesena was renewed and Garritano remained in Inter U19 team for 2012–13 season.
Garritano made his first team debut on 4 October 2012 in 2012–13 UEFA Europa League. Garritano made his debut in Serie A on 21 April in San Siro verse Parma.
In June 2013 the co-ownership of Garritano was renewed again. In July 2013 Garritano joined the pre-season camp of Cesena. Circa his graduation from the youth system his also signed a new professional contract with Cesena.
Garritano made 25 appearances for Cesena in 2013–14 Serie B; he also played 3 times in for the winner of the promotion playoffs. In June 2014 the co-ownership was renewed again. However, he only played 6 times in 2014–15 Serie A; on 9 January 2015 he was signed by Serie B club Modena in a temporary deal.
In June 2015 Cesena acquired the remaining 50% registration rights of Garritano from Internazionale, for another €50,000 fee. Internazaionale, its directors Piero Ausilio and Rinaldo Ghelfi were also fined by the Italian Football Federation in July 2016, for the price tags of Caldirola, Garritano and Nagatomo, for a total fine of €90,000. It was accused by the prosecutor that the price tags were inflated, in order to boost the club's financial positions of 2010–11 and 2011–12 financial year.
On 29 June 2017, 1 day before the end of Cesena and Chievo's financial year, Garritano, Rodríguez, Rigione and Daniele Grieco of Cesnea was sold to Chievo for Kupisz, Filippo Zambelli, Pietro Borgogna, Lorenzo Placidi and Carloalberto Tosi. Additionally, Lamin Jallow moved to Cesena on a temporary deal, with an option to purchase at the end of 2017–18 season.
Garritano was a member of the Italy U19 team at the 2013 UEFA European Under-19 Football Championship qualification and elite qualification, in which he made 4 appearances. He also played 3 friendlies for the U19 team, including the first match of the season, against Croatia U19.
On 8 October 2015 he made his debut with the Italy U21 squad, in a 3–0 win against Slovenia.
In June 2017, he was included in the Italy under-21 squad for the 2017 UEFA European Under-21 Championship by manager Luigi Di Biagio.Inter U19
Campionato Nazionale Primavera: 2012
Campionato Nazionale Dante Berretti (wildcard group): 2012