Mulder was born in Baarn, and is a product of Feyenoord's youth academy. In 2004, he started playing for Feyenoord's satellite team SBV Excelsior.
Mulder made his debut in professional football, as part of the Excelsior Rotterdam squad in the 2004–05 season. For two seasons there, he made 46 caps, scoring 4 goals.
In 2006, Mulder started playing for RKC Waalwijk. For five seasons he became an irreplaceable part of the right part of the defense, making 153 or more caps and scoring 4 goals. Mulder left Waalwijk at the end of the 2009–10 season, when his contract expired.
On 30 June 2010, Mulder agreed to join Bulgarian side Levski Sofia. On the following day he made his unofficial debut in a friendly against Metalist Kharkiv, before signing a two-year contract on 2 July as a free agent. He made his competitive debut on 22 July in a 2–0 away win over Dundalk in the second qualifying round of the 2010–11 UEFA Europa League.
On 8 December 2011, Mulder signed a one-year contract extension, keeping him at Levski until 2013.
He scored his first goal for Levski on 25 August 2012 in a 2–0 win against Montana at the Ogosta Stadium. In January 2013, it was reported that Mulder had extended his contract with Levski. The new two-year contract was signed on 15 January. Mulder ended 2012–13 season with a total of 5 goals.
In the summer of 2013 he was temporarily released from Levski, but was reinstated to the first team a month later.
In December 2013 during a game vs CSKA Sofia for the Bulgarian Cup, Mulder scored the last penalty for his team in the 7–6 win which led the team to the quarterfinals of the tournament. Mulder made his last appearance for Levski Sofia on 24 May 2014, after replacing Elin Topuzakov in the first half of a 3:2 win over S.S. Lazio in an exhibition match, which was held in commemoration of 100 years since the founding of the "blues". In the beginning of June 2014 new appointed sports director of Levski announced that the "bluemen" will no longer use Dustley's services as player. After 4 years of playing for the Bulgarian club, Mulder made 95 appearances in which he scored 2 goals.
In July 2014, Mulder signed a 1+1-year contract with Cypriot club Apollon Limassol. He made his official debut on 21 August 2014, in the 1:1 home draw with Lokomotiv Moscow in a UEFA Europa League match after coming on as a substitute during the second half.
Mulder made his debut for the Curaçaoan national football team in a qualification match for the 2018 World Cup against Montserrat on 28 March 2015.As of 9 January 2014.
Mulder plays as a right back and a right wing back.Curaçao
Caribbean Cup: 2017