Biuković made his debut in 1987 with the strip Dokaz published in the third issue of Croatian magazine Patak. He spent several more years working on comic projects in Croatia and collaborated with his good friend Darko Macan on the pages of German magazine Gespenster Geschichten. Most of those stories were later translated to Croatian (and collected into one volume titled Citati), as well as English (reprinted in various issues of Caliber's Negative Burn).
His big break came in 1994 when Dark Horse published Grendel Tales: Devils and Deaths, his another collaboration with Macan. The pair were subsequently asked back to do a four-issue sequel, Devil's Choices. In 1995, Biuković was nominated in the Best Penciller/Inker category and awarded the Russ Manning Best Newcomer Award in 1995.