[9][10] In November 2012, Dossaev joined the ruling Nur Otan party, upon which his membership card was presented by his Economic Development and Trade Minister Bakhytzhan Sagintayev.

[14] Dossaev announced on 20 March 2006 that tests had confirmed that a dead swan found in Mangystau Region, on Kazakhstan's Caspian Sea coast, had bird flu.

[17] Dossaev was dismissed as Healthcare Minister amid scandal after 81 children in south Kazakhstan were infected with HIV due to poor sanitary conditions.

[19] As the Minister of Economic Affairs, Dossaev oversaw a project to expand the production capacity of TengizChevroi (TCO), Kazakhstan's largest oil producer.

[5] In late 2015, Dossaev announced numerous agricultural reforms including changes to farm subsidies, improved crop insurance, and the introduction of electronic receipts designed to make the grain industry more efficient and profitable.

His proposals were made amid an economic slowdown due to low oil prices; as the Kazakh government responded with measures designed to diversify the country's economy.

"[21] Dossaev resigned from his post as Economic Affairs Minister in early May 2016 after public protests against the proposed bill that would have allowed foreigners to rent farmland for limited periods of time.

As part of his work at Baiterek, Dossaev was appointed to chairman of the board of directors of KazExportGarant, a state owned export insurance firm.

[26][27] While serving as head of Baiterek, Dossaev attended an international economic forum in Beijing to discuss China's Belt and Road Initiative in 2017.

"[36] According to Vlast.kz editor Vyacheslav Abramov, Dossaev would go on to serve as a "crisis manager" in his new position as he faced new task in leading a municipality for the first time by restoring public trust,[37] while Almaty grappled with the aftermath of the 2022 Kazakh unrest in which the city was most severally impacted in result, with 112.6 billion tenge worth of damaged administrative buildings, as well as looted shops and banks.

[41] According to Abramov, Dossaev's experience would help him to build relationships with businesses in Almaty in which the city depends on its budget while political scientist Dosym Satpaev suggested that if the Kazakh government had introduced direct äkım elections, then there would've been "powerful competition and worthy candidates" instead.

[43] He vowed to quickly restore the city after the riots by providing compensation to local business owners, ensuring public safety by installing more surveillance cameras, increase street lighting, creation of more jobs and more incomes to the city populace, stabilize food prices, construct more education facilities, improve healthcare equipment and infrastructure, acquire newer environmentally clean municipal bus fleet, continue planting more trees, repairment of city roads, continued development in new incorporated areas and solve urban sprawl issues.

[43] Dossaev is the co-founder, longtime financial supporter, and board member of the Alumni Fund of the Republican Physics and Mathematics school (RPMS).