His work was a combination of two styles; Alpine, showing the influence of Thomas Schwanthaler [de] and Meinrad Guggenbichler [de], and Italian, with influences that can be traced to Gianlorenzo Bernini and Giuseppe Maria Mazza.
The only fully-documented influence on him came from the painter and engraver, Gottfried Bernhard Göz, who also worked at the Abbey and provided the sketches for some of Stammel's sculptures.
He used wood, as well as stone, often modelled in wax, and his figures are noted for their strong emotional expressions.
Although "Thaddäus" is sometimes given as his middle name, it was apparently a nickname of unknown origin.
It first appeared in 1834, in a work by Ignaz Kollmann (1775-1837), a poet and novelist who also wrote art criticism.