Born in Tiflis (modern Tbilisi), Mantashev spent most of his childhood in Tabriz, in northern Iran, where his father was involved in the cotton and textile trade. Being the only son, he was involved in his father's business affairs early on. In 1869, he moved to Manchester (known as Cottonopolis in the 19th century), a major center of cotton and textile processing industries, from where he helped ship goods to his father in Tabriz. Mantashev's stay in Manchester played an important role in the development of his character. Not only did he learn the secrets and crafts of the textile industry in Manchester, but he also delved into the intricacies of European business and English culture. During this period he learned the English, French, and German languages. In 1872, Mantashev returned to Tiflis with his father. In the first floor of the hotel Caucasus, located in Erivansky Square, the Mantashevs opened a cotton store, then another one, eventually becoming fully engaged in the wholesale textile trade. After his father's death in 1887, Alexander purchased most of the shares of the Tiflis Central Commercial Bank — thus becoming its principal shareholder, and then the Chairman of the Board of the Bank. The bank was involved in almost every aspect of trade in the Caucasus. Incidentally, Tifkombank was the only financial institution in the Caucasus whose shares traded on the Saint Petersburg Stock Exchange. In the early 1890s, Alexander was already a 1st guild merchant and a Speaker of the Tiflis duma. It was then that he became interested in a new business venture, when he was looking into the prospects of Baku oil.
This was the epoch of the world oil trade. The underground black liquid promised entrepreneurs incredible profits and opened ambitious prospects. The only requirements were a large investment and the ability to run the business. These Mantashev had. His chief accountant recalled that not a single document went into effect without Alexander's resolution, "Asttsov" ("with God" in Armenian). Mantashev, not being afraid of high risk investments, bought (together with another Armenian colleague, Michael Aramyants) unprofitable oil wells in Baku that very soon became profitable. In 1894 he created a tentative association along with the other major oil interests in Russia, the Nobels and the Rothschilds, in order to cooperate in the marketing of petroleum products within certain geographical areas. This was in response to Standard Oil's aggressive marketing policy. In 1896, during a trip to Egypt, Mantashev met Calouste Gulbenkian who was fleeing the Ottoman Empire with his family as a result of the Hamidian massacres. Mantashev introduced Gulbenkian to the right circles in Cairo, including Sir Evelyn Baring. For refining oil, Mantashev built a kerosene plant in Baku, as well as a lubricant plant and a marine refinery for pumping oil and fuel to vessels. His company owned a factory for the fabrication of canisters for the packaging and storage of oil in Batumi, a mechanical workshop in Zabrat, an oil pumping station in Odessa, and even one hundred freight cars circulating in the southwestern railways of Russia. (The young Joseph Stalin organized strikes in Mantashev's Batumi factory and participated in street demonstrations in 1902.) In England Mantashev bought two tankers, which supplied oil to India, China, Japan and the Mediterranean countries. In 1899 he created the trading house "A.I. Mantashev and Co.", opening representative offices and warehouses in the major cities of Europe and Asia: Smyrna, Thessaloniki, Constantinople, Alexandria, Cairo, Port Said, Damascus, Paris, London, Bombay and Shanghai. Mantashev became a shareholder in a number of oil companies, among them the Nobel Brothers. 51.3% of the total stock of oil and 66.8% of the oil content in the Caspian Sea was centered on the firm. In 1904, it was the third largest oil company in Baku, next to only the Nobel Brothers and the Caspian Sea Society of the Rothschild brothers.
Once while riding on a train from Vienna to Paris, Mantashev was accompanied by a silent passenger in the same car. Mantashev failed in all his attempts to communicate with the passenger. Only when it came to the subject of Baku oil did the silent passenger become talkative. During their discussion he had asked several professional questions regarding oil and had mentioned that the only person he had heard of in Baku was Alexander Mantashev. Mantashev smiled and introduced himself. The conversation stalled thereafter. In Paris, they shook hands and parted. A few days later Mantashev was invited to a cocktail party by Britain's Baron Rothschild. It became clear that the Baron had been the silent passenger on the train because the personal invitation contained several lines regarding their encounter on the train.
Mantashev funded the Baku-Batumi pipeline which was launched in 1907, becoming the world's longest pipeline, 835 kilometers long. From 1899 to 1909, his company by volume of fixed capital (22 million rubles) was the largest in Russian industry. It is said that before buying oil wells Mantashev personally examined them. He knew that a rich deposit may suddenly dry up, and vice versa: a well seemingly lacking in prospects could end up as a rich fountain. Surrounded by a group of geologists and petroleum engineers, he visited the sites asking countless questions, carefully studying land-color, softness etc.; he even smelled the land. Mantashev always inquired into the status of the neighbouring sites, often seemingly choosing them at random and saying : "It's here, start digging." No one could understand what it was that made him choose that particular spot. But his decision was always final. The great paradox was that when drilling commenced, an oil fountain was almost always discovered.
Along with twelve like-minded people he founded the "Armenian Charitable Society in the Caucasus". He donated 300,000 rubles towards the building of the Nersessian spiritual academy. He donated 250,000 rubles to the holy town of Echmiadzin for the building of the residence of the Catholicos of All Armenians (construction completed in 1914). Mantashev hand-picked fifty talented young Armenians and sent over two hundred to study at the best universities of Russia and Europe. Among them was the famous Armenian composer Komitas, Hrachya Acharyan and the controversial Communist revolutionary Stepan Shahumyan as well as others who became famous later on. The most famous donation made by Mantashev remains the Armenian Church of St. John the Baptist in Paris on Jean Goujon street. He explained that he chose Paris because that's the city where he sinned most. During its construction in 1904 Mantashev spent 1,540,000 francs. For this act, the President of France gave Alexander Mantashev the Order of the Legion of Honor.
Despite all of his wealth Mantashev led a modest lifestyle. He did not like gold and never wore jewellery. He only attached a fresh flower to his vest. He did not have an entourage and enjoyed travelling by tram in Tiflis. It is said that Mantashev only carried with him 20 gold coins and five rubles. Mantashev loved the theatre. In Tiflis he built the Pitoewski Theatre (now the Rustaveli Theatre). In the Academie National de Musique of Paris he had a personal lounge. He intended to build a similar theatre in Yerevan. The Small Hall of the Armenian Philharmonic Orchestra was also built by him. Mantashev died on 19 April 1911 in Saint Petersburg. His body was moved to Tiflis and buried next to his wife at the cemetery of Van Cathedral which was being restored at the time with his donations. After the October Revolution of 1917, his company ceased to exist along with all the other oil companies in Russia. In 1933, by the order of Lavrentiy Beria, the Van Cathedral was destroyed along with the cemetery where Mantashev was buried. Today he is remembered in Tbilisi for his charity, where many of his buildings are still standing, and in Yerevan, where a downtown street was named after him along with a major luxury goods store. A monument of Mantashian has been erected in Yerevan in April 2012.