Born in Fürth, in his youth Beiersdorfer played for TSC Cadolzburg, TSV Altenberg and ASV Herzogenaurach. In 1984, he moved from 1. FC Bamberg to Oberliga team SpVgg Fürth, where he was discovered by scouts of Hamburger SV. Beiersdorfer was soon lured to Hamburg along with his friend Manfred Kastl. Immediately Beiersdorfer was able to gain a place in the first eleven, and he would subsequently help Hamburg to win several matches and the German cup.
