Born in the town of Jesenice in a family of athletes—skiing coach father Dušan Blažič and mother Ksenija who had formerly played volleyball—young Jaka took up basketball early.

[10] As a member of the senior men's Slovenian national basketball team, Blažič competed at the EuroBasket 2013 and 2014 FIBA World Cup.

In the early morning hours of Saturday, 4 October 2014, Blažič caused a traffic accident while driving under the influence, slamming his Volkswagen Golf into the back of a taxi vehicle while changing lanes at the corner of Nemanjina and Resavska streets in central Belgrade.

No injuries were reported as the traffic patrol administered a breathalyzer test on the twenty-four-year-old KK Crvena zvezda basketball player, determining his blood alcohol level was above the 0.5‰ legal limit in Serbia.

[13] Several hours earlier, Friday evening 3 October 2014, Blažič had played in KK Crvena zvezda's opening game of the 2014–15 Adriatic League season versus Levski Sofia,[13] an 85-55 blowout win in which he contributed 8 points including a spectacular dunk.