In 2011, Murakami became the first to land the quad salchow jump in the men"s category at the Japan Championships. The Murakami family moved to the United States in 2000 from Japan after winning a green-card lottery to become United States residents. Daisuke, nicknamed "Dice", began skating soon after.
Murakami is a two-time recipient of the Michael Weiss Foundation scholarship, which is a scholarship program created to help young American figure skaters.
Murakami began skating at age ten. He began competing on the juvenile level in 2001.
In 2010, Murakami parted ways with his coach Nikolai Morozov and relocated to work with Frank Carroll in Los Los Angeles The following season, Murakami placed first at the 2011 Ondrej Nepela and at the 2011 Merano Cup.
He then finished sixth at the 2011 Skate America and at the 2011-2012 Japanese Nationals.
Murakami began his 2012-2013 season by winning the silver medal at 2012 Ondrej Nepela. During competition at the 2012 Nippon Hōsō Kyōkai Trophy, Murakami dislocated his right shoulder forcing him to withdraw from the event. He then withdrew from the 2012-2013 Japanese Nationals for recovery, but came back to finish the season with a bronze medal at the 2012 Triglav Trophy.
Murakami came in tenth at the 2013-2014 Japanese Nationals.
He finished the season with a gold medal at the Printemps, in Luxembourg. On August 12, 2014, it was announced that Murakami had been selected as a host pick at the 2014 Nippon Hōsō Kyōkai Trophy.
In September, he placed third in the 2014 United States. International Classic at Salt Lake City, Utah.