Cuevas began his career at Primera División de Chile club O'Higgins. He progressed from the club's youth level all the way to the senior team. In 2011, he was promoted to the senior team, making his debut on 8 May in a 5–1 away loss to Colo-Colo at the Estadio Monumental. Cuevas has continued to appear since it, particularly in Copa Chile games. In November 2012, it was reported that Cuevas had held a successful trial with Premier League clubChelsea following a number of impressive performances for the Chilean under-20 team. In 2013, after a season at the reserve team, he was considered by Eduardo Berizzo to play the Torneo Transición, who chose him after a well South American Youth Football Championship in Argentina with the national under-20 side. He made seven appearances and before the FIFA U-20 World Cup, on 23 July, Cuevas completed a five-year contract with Chelsea which will keep at Stamford Bridge until 2018. The English club paid a £3 million fee for the player.
On 1 September 2013, Cuevas made his first appearance on the bench in the match against AZ, although he was an unused substitution as Vitesse drew 1–1. On 1 September 2013, he again made an appearance on the bench in the match against PEC Zwolle, but remained unused. Cuevas failed to make a single first team appearance before Vitesse decided to cancel his loan in February.
On 7 February 2014, it was announced that Cuevas would spend the rest of the season on loan with FC Eindhoven in the DutchEerste Divisie. Later that day, he made his debut, coming off the bench and replacing Torino Hunte after the first half in a match against Almere City which ended in a 2–1 loss for Eindhoven. On 28 March, he scored his first goal for the club – and his first professional goal – in a 4–0 win over Sparta Rotterdam. He finished the season with 13 appearances and one goal.
On 30 June 2014, Cuevas was sent on a season long loan to Universidad de Chile. He made his debut on 13 February 2015 against Unión Española, which ended in a 2–1 loss for Universidad de Chile. Cuevas made a total of six appearances with only four league appearances during his time back in his home country.
Loan to Sint-Truidense V.V.
On 10 August 2015, Cuevas was sent on a season-long loan to Belgian side Sint-Truiden along with fellow Chelsea youth player Joao Rodríguez. On 16 August 2015, Cuevas made his debut off the bench in the 62nd minute, replacing Yannis Mbombo in the match against Gent, a 1–0 defeat. On 21 November 2015, Cuevas scored his first goal for Sint-Truiden in their 2–1 away defeat against Waasland-Beveren, netting the opener of the fixture in the 9th minute. On 31 August 2016, Cuevas returned to Sint-Truiden for another season-long loan.
Huachipato
On 1 July 2017, Cuevas agreed to return to Chile to join Primera División side Huachipato and a month later joined Dutch side Twente on a season-long loan. On 14 April 2018 he became the joint record holder for most yellow cards in a single Eredivisie season after getting his 12th yellow card of the season against ADO Den Haag. Following an season at Twente, Cuevas joined Austria Wien in July 2018 on a season-long loan with an option to buy.
