Spinelli began his career as a goalkeeper coach at local team Como in 2002; as a player, he had previously served as a reserve goalkeeper for the club behind Alex Brunner, and helped the team achieve promotion to Serie A in 2002, starting in his side's decisive 2–0 home win over Empoli at the Stadio Giuseppe Sinigaglia, and keeping a clean sheet. After spending two years with the Lariani, he was picked up by Serie A team Genoa C.F.C.. He spent 12 years at Genoa, serving under 16 managers, and coaching several goalkeepers, and helping lead the club out of the Serie C, to the top flight; during his time with the club, he earned a reputation as one of the best goalkeeping coaches in Italy. From 2014 Spinelli joined manager Antonio Conte as part of the coaching staff of the Italy national football team, maintaining the dual role of goalkeeping coach for both Genoa and Italy. After Italy's 6–5 penalty shootout loss to Germany in the Euro 2016 quarter-finals, Spinelli followed Conte to English club Chelsea. He held the dual role of goalkeeping coach for both the Italy national football team and Chelsea. During the 2016–17 Premier League season, Chelsea's starting goalkeeper Thibaut Courtois praised Spinelli's abilities as a goalkeeping coach, and has credited Spinelli for helping him to improve his overall game and technique, in particular his foot-work and diving, which enabled him to be more explosive and get to ground more quickly. The team's back-up goalkeeper, Asmir Begović, also praised Spinelli throughout the season, commenting: "He came in with a big reputation, we had heard a lot of great things about him and the work he did in Italy, especially with the national team during all those years at Genoa. I was excited to work for him and it's been a pleasure since day one. He's a really good guy, he creates a great atmosphere, and he really knows what he is talking about." Chelsea finished the season as Premier League Champions. The following season, Chelsea won the FA Cup. After Antonio Conte was sacked by Chealsea in July 2018, Spinelli joined Paris Saint-Germain as the team's new goalkeeping, where he was re-united with former Italy goalkeeper Gianluigi Buffon. He continued to hold a dual role as both Paris Saint-Germain's goalkeeping coach, and the goalkeeping coach of the Italian national team, under manager Roberto Mancini.
