Alexander Grosz was born in Neusatz (Novi Sad/Ujividek) in present-day Serbia. He attended the watchmaking school in Karlstein an der Thaya from 1884 to 1887, then worked with his uncles Max and Gezá Klumak, also from Neusatz, who made chronometers for the Austrian navy and were among the pioneers of precision watchmaking in Austria. Between 1893 and 1902 he worked with prominent watchmakers in Frankfurt am Main, Rome, Cairo and Paris. In 1902 he moved to Vienna opened an independent workshop in the 1st district, first at Färbergasse 10 and then at Wipplingerstraße 17, where he also had an antiques dealership specializing in watches and clocks. While in Paris, he had already started collecting historical timepieces, a passion he shared with Marie von Ebner-Eschenbach, whose watchmaker he was. He was a member and chairperson of the Verein der Freunde des Uhrenmuseums (Association of Friends of the Clock Museum) in Vienna, founded in 1917. He was also a member of the editorial board of the magazines Die Uhrmacherkunst and Uhrmacher Fachblatt and wrote numerous articles for them. He donated and acquired timepieces and parts for the Clock Museum. Between the wars he also gave lectures at the Technisches Museum Wien and had radio broadcasts with music boxes on Radio Wien.

After the annexation in March 1938, Grosz was persecuted and by the Nazis. Josef Berger, the kommissarischer Verwalter (provisional administrator) appointed by the Vermögensverkehrsstelle (Property Transaction Office) to liquidate the company offered the antique timepieces and collection for sale by agreement with the watchmakers' guild to the watchmaker and guild master Eugen Ritter in Feldkirch, Vorarlberg, and to the Vienna Clock Museum. The remaining stocks were given to the Einkaufs- und Treuhandgenossenschaft für die Uhren- und Juwelenbranche (Purchasing and Trustee Cooperative for the Watchmaking and Jewellery Industry) on Schwedenplatz. On 28 October 1938, Rudolf Kaftan, director of the Clock Museum, personally took seventy watches from Grosz's home. Berger misappropriated the money he had received for the antique timepieces, collection and stocks and left Austria with his family. As he had sold them for less than their true value, the Abwicklungsstelle für die Liquidation und Arisierung des Uhren- und Juwelenfaches (Processing Office for the Liquidation and Aryanization of the Clock and Jewellery Sector) demanded additional payments from Grosz, which he could not pay because his entire assets had been looted. Grosz and his wife Clara managed to escape with their daughter Gertrude and her husband Sigmund Ackermann to the USA on 30 October 1939 to the USA. Grosz died a few months later in New York at the age of seventy.

Because of looting by members of the Red Army in the parsonage of Klein-Engersdorf in 1945, where most of the timepieces from the Städtische Sammlungen Wien were stored, thirty of the timepieces from the Grosz collection disappeared. Following systematic provenance research in Wien Museum, the Vienna Restitution Commission determined on 1 July 2003 that the remaining forty timepieces were eligible for restitution. After a long search for heirs, they were finally returned to Alexander Grosz's legal successors in 2013.