Kammala jumla mai zuwa: Vujasinović ya fara bugawa tawagar kasa wasa a Kotor inda ya ci kwallo ta farko a wasan da suka yi da Faransa a nasarar da suka ci 18 da 3. Yana da shekara 17 da wata uku da kwana 22. Daga 1995. Ya kasance memba na dindindin na tawagar 'yan wasa, kuma kyaftin tun 2003. A wannan lokacin, Vladimir ya rasa kawai
Gasar zakarun Turai ta 1999 bayan wata badakalar doping bayan wasan kusa da na karshe na gasar cin kofin Italiya. A cikin bincike da yawa, an zabe shi a matsayin mafi kyawun dan wasan polo na ruwa a duniya bisa dalilin cewa zai iya yin wasa daidai a duk matsayi don ƙungiyar. Mafarki na duk mai kunnawa, ya kasance memba na duk abubuwan da za a iya tsarawa. Ya yi ritaya daga tawagar kasa a shekarar 2008. Ana ɗaukar Vujasinović a matsayin ɗaya daga cikin mafi kyawun playersan wasa a cikin tarihin wasan polo na ruwa na duniya. Ya buga wa kungiyar kwallon kafa ta Croatia Primorje, ta Serbia VK Crvena Zvezda, ta Spain Barcelona, ta Italiya AS Roma Pallanuoto, ta Serbia VK Partizan, ta Italiya Pro Recco, ta Brazil Fluminense. A lokacin rani na 2007 ya buga wasan tare da kungiyar Maltese ta Neptunes WPSC kuma ya taimaka musu su ci gaba da gasar Maltese First Division. An kira shi "Mai Girma Mai Girma" a gasar zakarun Turai ta 2001 a Budapest, Hungary. Vujasinović ya lashe gasar zakarun Turai sau da yawa tare da Pro Recco na Italiya (shekara ta 2007 da 2008) da kuma VK Partizan na Serbia. Ya koma Partizan Belgrade don kakar 2008 / 9. Ya lashe gasar Malta Waterpolo Summer League tare da Neptunes Emirates (St. Julians, Malta) a watan Agusta 2010.