Alexander Slutskiy graduated from the Novosibirsk Conservatory as a violinist. While at the conservatory he played in the Novossibirsk Symphony Orchestra conducted by Arnold Katz.
In 1969-1973 he was a soloist of the Kemerovo State Philharmonic. In 1973 he started his career at the State Symphony Orchestra of the USSR conducted by Evgeny Svetlanov. Under Svetlnov's great artistic influence Alexander Slutskiy started learning orchestra conducting and graduated from the East Siberian State Academy of Culture and Arts with opera and symphony conducting degree. After taking a workshop with the Finish conductor Jorma Panula he started working with several Moscow orchestras as a conductor including the Moscow symphony orchestra, Young Russia orchestra (now New Russia Orchestra), and the Chamber Orchestra Kremlin.
In 2003 he was invited to work with the State Symphony of Russia named after Evgeny Svetlanov. Alexander Slutskiy also managed the Young Talents subscription series at the Moscow Philharmonic Hall. He pays a lot of attention to the music of modern composers and his concerts received praise of such composers as Tikhon Khrennikov, Rodion Schedrin, Andrey Eshpai...
In 2004 Alexander Slutskiy was awarded the title of Honored Artist of Russia. In 2008 he was awarded the Medal of St. Prince Daniel of Moscow and in 2012 he received a Medal of the Order of Merit to the Fatherland. As a conductor he toured in the USA, Spain, the United Kingdom, Turkey and the countries of the former Soviet Union.