The early Flemish biographer Karel van Mander states in the Schilder-boeck (1604) that de Punder was the pupil of the Mechelen painter Marcus Willems (1527-1561). Willems had been a disciple of Michiel Coxie, one of the leading Romanist painters in Flanders who had helped introduce Italian Renaissance painting there. Willems married de Punder's sister Katharina.
De Punder married Barbara (Barbel) Verhulst. She was the sister of Lysbeth Verhulst, the first wife of the painter and engraver Hubert Goltzius. De Punder and Goltzius would occasionally collaborate on commissions.
He worked in Leipzig in 1570 before moving to Denmark, where he later died.