[2] He grew up in Hallstatt and later published about the archaeological plant remains from the Late Bronze- and Iron Age mines[4] that had been uncovered by his father.

Stapf studied botany in Vienna under Julius Wiesner, where he received his PhD with a dissertation on cristals and cristalloids in plants.

He published the results of an expedition Jakob Eduard Polak, the personal physician of Nasr al-Din, the Shah of Persia, had conducted in 1882, and plants collected by Felix von Luschan in Lycia and Mesopotamia 1881–1883.

Ergebnisse der Polak'schen Expedition nach Persien" (Memoirs of the Imperial Academy, Vienna, 1885–1886); "Beiträge zur Flora v Lycien, Carien u Mesopotamien" (ibid., 1885–1886); "Die Arten der Gattung Ephedra" (ibid., 1889); "Pedaliaceae and Martyniaceae" (Engler and Prantl's Die Natürlichen Pflanzenfamilien, 1895); "Flora of Mount Kinabalu in North Borneo" (Trans Linn Soc, 1894); "Melocanna bambusoides" (ibid., 1904); "Structure of Sararanga sinuosa" (Journ Linn Soc, 1896); "Dicellandra and Phaeoneuron" (ibid., 1900); "Monograph of the Indian Aconites" (Annals, Royal Botanic Garden, Calcutta, 1905).

In 1913 botanist Ernest Friedrich Gilg published Stapfiella, which is a genus of flowering plants from Tropical Africa belonging to the family Passifloraceae and named in his honour.