Born in Amsterdam as the son of a wealthy Catholic family, Vopiscus (a name usually given to the surviving half of a twin) Plemp was educated by the Jesuits at Ghent and studied at Louvain (with Fromondus) and Leiden (with Vorstius), before embarking on a European tour, which brought him to Padua and Bologna. After taking his medical degree at Bologna (1624), he started a medical practice at Amsterdam. In 1633 he was appointed professor of medicine at Louvain, where after a successful career he also died. Plemp was a very learned man who, thanks to his knowledge of oriental languages, could enrich the Galenic tradition with elements from Arabic medicine.

Plemp knew Descartes during the latter's Amsterdam years (1630–31). They became friends, and Descartes turned to him to collect the objections he originally planned to publish as a sequel to the Discourse on Method and “essays” (1637). Apart from the objections written by himself, Plemp was also Descartes’ intermediary with his Louvain colleagues Fromondus and Ciermans. In his own objections, Plemp concentrated on the circulation of the blood and the movement of the heart. Although in the course of his correspondence with Descartes, Plemp gradually came round to the ideas of William Harvey (1578–1657) on the circulation of the blood (Descartes even offered to add a note to the effect that the arguments against circulation were proposed only for the sake of argument; see AT II 344), he remained resistant on the subject of the movement of the heart. According to him, this could never be caused by the fact that the blood is heated in the heart because the latter continues to react to stimuli long after it is removed from the body, even in cold-blooded animals. In his replies, in which he refers to vivisection on rabbits and eels, Descartes is forced to introduce other factors, like the specific quality of the blood of fish and similar animals. Even so, in a letter to Mersenne Descartes praised Plemp's objections, which according to him covered all the relevant points (AT II 192, CSMK 105). Descartes broke with Plemp when the latter published excerpts from their correspondence in his Fundamenta seu Institutiones Medicinae (1638), not only because it thwarted his own plans for a sequel to the Discourse but also because in his view Plemp had “mutilated” their exchange.