He is the Sri Lankan national record holder in every single freestyle event, the 200m and 400m Individual Medley, and the 50m Butterfly.

His brothers, Andrew, Dillon and Kyle Abeysinghe, are all past and present members of the Sri Lankan National swimming team.

In 2011, Abeysinghe represented Sri Lanka three times; at the 2011 World Aquatics Championships, the 2011 Youth Commonwealth Games, in the Isle of Man, making it to the finals of the 400m Freestyle, and Asian Age Group Swimming Championships, where he won the silver medal in 100m Freestyle.

After setting a national record in prelims, he advanced to the semi-final, where he raced amongst the likes of future Olympians; Duncan Scott and Kyle Chalmers.

Abeysinghe competed at the 2016 Summer Olympics in Rio de Janeiro, Brazil, alongside fellow swimming star, Kimiko Raheem.

At the 2018 Commonwealth Games in Gold Coast, Australia, Abeysinghe was a part of the 4×100 Freestyle relay for Sri Lanka.

Again, he was a part of the 4 × 100 m Freestyle relay team alongside his brother Kyle, Akalanka Pieris and Cherantha De Silva.

[8] Abeysinghe overcame training challenges due to COVID and competed in the 50 and 100 Freestyle events at the postponed Summer Olympics in Tokyo in 2021.

After a break from swimming, Abeysinghe stormed back in dramatic fashion taking the top spot on the Sri Lankan National Team to qualify for the 2023 World Aquatics Championships in Fukuoka, Japan.

Continuing on from the success he had in Fukuoka, Abeysinghe represented Sri Lanka at the 2023 Asian Games where broke the 50m Butterfly National record, previously held by Akalanka Peiris.

[11] He then joined Asian International School Colombo, subsequently moving to the US for higher education and training at The Ohio State University.

His youngest brother, Kyle Abeysinghe, is a two-time silver medalist at the Youth Commonwealth Games, one of few Sri Lankan athletes, and only swimmer, to ever achieve such a feat.

Mathew trained out of the CR&FC's swimming pool in Colombo, and his team Killer Whale Aquatics is a dominant force in the local swimming arena, where they have won the men's national championship on 5 consecutive years since 2015 and the women's national championship on 5 occasions as well.