Sammoutis joined the Millwall academy at the age of 15, and went on to play for the Under-18s and Under-21s. In March 2013, he was released after failing to be offered a professional contract. Sammoutis trained with Isthmian Premier Division club Margate in pre-season following his departure.
In August 2013, Sammoutis joined Isthmian Premier Division side Metropolitan Police. He made his senior debut in a 2–1 defeat at Enfield Town on 10 August, and went on to make six appearances for the club.
Margate
Sammoutis joined league rivals Margate, alongside former Millwall teammate Daniel Newman, in September 2013. He scored his first senior goal in a 2–1 defeat against Bury Town on 12 October. A week later, he scored two goals in a 9–4 FA Trophy win at Wroxham. In June 2014, Sammoutis left Margate by mutual consent in order to return to Cyprus of personal reasons.
In August 2014, Sammoutis joined Cypriot First Division club AC Omonia. Scoring the only goal in a 1–0 pre-season victory at Nea Salamis Famagusta, he marked his league debut with an assist in the final minute to earn a 1–0 victory against Othellos Athienou. Sammoutis made a total of five appearances for the club, into two Cypriot Cup fixtures.
In July 2015, Sammoutis returned to England and joined Isthmian Division One South club Walton Casuals two months later. He scored eight times in 33 appearances in his inaugural season, and was rewarded with a trial at League Two club Barnet in March 2016. After returning for a second trial in the summer, he spent pre-season with National League side Bromley, but committed to Walton Casuals for the 2016–17 season.
Sammoutis completed a move to league rivals Greenwich Borough in May 2017. Making his debut in a 1–1 draw with Whyteleafe on the opening day of the season, he scored his first goal for the club in a 4–1 Kent Senior Cup win at Ramsgate a week later. On 28 August, he scored a brace in a 3–0 win against Phoenix Sports. Sammoutis was dismissed for the first time in his senior career during a 4–0 win against Guernsey on 23 December.
Walton Casuals
In February 2018, Sammoutis rejoined league rivals Walton Casuals. On 17 February 2018, he made his debut in a 2–1 win against South Park – the same opponent and scoreline from his first debut for the club. A week later he scored his first goal since returning to the club in a 3–2 defeat to Whyteleafe and added another in the subsequent 2–2 draw with Guernsey. On 17 April, he completed the scoring in a 2–0 win at Shoreham. Named as a substitute in the Isthmian League South Division Play-Off Semi-Final, Sammoutis came off the bench and scored the final goal of a 5–2 victory in the 90th minute. He was then rewarded with a start in the Play-Off Final at Corinthian-Casuals as his team went on to secure promotion with a penalty shoot-out. On 15 May, Sammoutis announced he would not return for the club for the 2018–19 season, citing the league restructuring and unfeasible travel times in a new division.
In May 2018, he joined Isthmian League South East Division club Hythe Town.
Greenwich Borough
On 14 March 2019, he returned to fellow South East Division club Greenwich Borough.
Cray Valley Paper Mills
He joined Cray Valley Paper Mills during the summer of 2019.
International
Sammoutis began his international career in November 2012, when he made his first appearance for Cyprus at Under-19 level in a European Championship qualifier. He went on to make a further four appearances at youth level.
