Graf was trained as a goldsmith in his father's workshop in Solothurn. In 1503 he headed for Strasbourg and Zurich on his journeyman's travels. In 1507 he is documented as an apprentice to the goldsmith Lienhart Triblin in Zurich, who also trained him as a stained-glass painter. In 1509 Graf worked in Basel, designing woodcuts for the city's printers. Starting in 1510 he took part in campaigns into northern Italy and Burgundy as a mercenary. In 1511 he married Sibylla von Brunn, who came from a patrician family in Basel. Graf was repeatedly arrested for mockery, fomenting nocturnal disturbances, and brawling. In 1512 he was accepted into Basel's goldsmiths' guild, in which he held an elevated office. From 1519 to 1523, he worked as a coinage die-cutter for the city of Basel. Graf's early work was influenced by the art of Schongauer, whose engravings he copied. Until 1515 he was the most sought-after book illustrator in Basel. His unusual stock of subjects and motifs reflects the everyday life of the city in the early sixteenth century as well as his numerous wartime experiences.