Biseswar made his professional debut for Feyenoord on May 22, 2005. After two spells as a loanee at Heracles (2006/2007-season) and De Graafschap (2007/2008-season) returned at Feyenoord. In January 2012 Biseswar signed a contract at Turkish side Kayserispor. In the summer of 2016 Biseswar signed for PAOK a three year contract on a free transfer.
In his first season Biseswar won the Greek Football Cup with PAOK beating AEK 2-1 in the final. Biseswar scored the first goal of the match and was voted man of the match. In 2018 he won the Greek Football Cup again. PAOK and AEK met again in the final and this time the score was 2-0 for the team from Thessaloniki.
On April 21, 2019 “The Artist” scored the second goal of PAOK in their 5-0 win over Levadiakos that brought the club the third League title after 1976 and 1985 with a socalled “Panenka” from the penalty-spot. As PAOK won the cup for the third time in a row in 2019 with AEK as the opponent again, he also won the first "double" in the club's history.
Biseswar has played for the Netherlands at under-16, under-17, under-19, under-21 and B-international level.
Biseswar played at the 2005 UEFA European Under-17 Football Championship in Italy, scoring a late group stage winner against Israel. The goal took the Netherlands through to the semi-final against hosts Italy. Biseswar was mentioned in the team of the tournament, but couldn't save his team from losing in the final to Turkey. With a second place, the Netherlands U17 qualified for the 2005 FIFA U-17 World Championship in Peru. Biseswar's team finished third after losing the semi final against later winner Mexico U17 (0–4), but winning the third place play-off match against Turkey U17 (2–1).
Biseswar was voted best left winger of the decade (2010-2020) by the fans of PAOK.