Verschaffelt was born in Ghent, Flanders in the Spanish Netherlands, as Pieter Antoon Verschaffelt. In 1748, he received the commission to replace the damaged statue of the archangel Michael on the Castel Sant"Angelo in Rome, although it wasn’t installed until 1753. In 1752 Verschaffelt moved to London.
From there, he was appointed as a successor to the sculptor Paul Egell as court sculptor to Charles Theodore, Elector of the Palatinate, in Mannheim, Germany.
Among his first tasks was the landscaping and statuary in the palace garden of Schwetzingen, for which he created the deer and the group of rivers, which are the key features of the park. He died in Mannheim, Electoral Palatinate, Holy Roman Empire, aged 83.