Son of King Murchad mac Finn and brother of Gormflaith, he belonged to the northern Leinster dynasty of the Uí Dúnlainge, and in particular the branch of the Uí Fáeláin whose lands lay around the town of Naas, anciently Nás na Rí, "the Assembly Place of the Kings" or Nás Laighean "the Assembly Place of the Leinstermen" on the middle reaches of the River Liffey, in modern County Kildare.
According to the account of the battle contained in Cogad Gáedel re Gallaib ("The War of the Irish with the Foreigners") King Máel Mórda died in single combat with Conaing mac Donncuan, King of Desmond, Brian Boru's nephew, as follows "We must next speak of Conaing.
His other son Bran mac Máelmórda was King of Leinster from around 1016 until he lost the kingship in 1018 after being blinded by his cousin the King of Dublin Sitric Silkenbeard son of Amlaib, after which Bran retired to Cologne, probably to the Benedictine monastery of Great St Martin which was run by Irish monks at the time.
The Annals of Ulster record in 1052 that "Braen son of Mael Mórda, king of Laigin, died in Cologne".
The Irish doom metal group Mael Mórdha take their name from Máel Mórda mac Murchada and many of their songs are based on the events of the Battle of Clontarf.