Born in Melník, Maŭr began his career working as an opera singer at the opera house in Klagenfurt in 1839. From 1842-1844
he worked at various theatres in Prague, after which he was committed to the opera house in Darmstadt from 1844-1846.
At the behest of Frantiek Ladislav Rieger, he returned to Prague in 1846 to become a principal singer at the Estates Theatre.
His singing was praised by Czech audiences but his acting was found to be wanting. He was eventually appointed
the house's chorus master at the beginning of the 1848-1849 season.
By 1851 Maŭr was no longer appearing in opera roles, but was now working as a conductor of a number of different musical ensembles
in Prague; including choirs in various cathedrals in the city (such as the Our Lady of the Snows Basilica). He left his position
as chorus master at the Estates Theatre in 1853 to focus on his career as a conductor.
He gained a great reputation in Prague for his conducting of sacred music during the 1850s.
In 1854 he was appointed as a teacher of singing at the Prague Conservatory.
In the autumn of 1862, Maŭr was appointed the first director/principal conductor of the Provisional Theatre, to the disappointment
of Bedrich Smetana, who had hoped for the position himself. The theatre opened on 18 November 1862, with a performance of
Vitezslav Halek's tragic drama King Vakusin.
Since there was at the time no Czech opera deemed suitable, the first opera performed at the theatre, on 20 November 1862,
was Cherubini's Les deux journées. For the first year or so of its life, the Provisional Theatre alternated opera with straight
plays on a daily basis, but from the start of 1864 opera performances were given daily.
Maŭr remained at the Provisional Theatre until September 1866; his tenure was marked by a professional rivalry with Smetana,
who criticised the theatre's conservatism and failure to fulfil its mission to promote Czech opera. Maŭr retaliated by refusing
to conduct Smetana's The Brandenburgers in Bohemia. A change in the theatre's management in 1866 led to Maŭr's removal and
replacement by Smetana.
He continued to be active as a conductor in Prague up until his death in that city in 1888.
Maŭr also produced a few musical compositions. Most of his output was in sacred music, but he also wrote two operas: Horymír
and Jaromír, vojvoda ceskŭ.