A pug mill is a machine consisting of a large cylinder with a central shaft passing through it from top to bottom.
In what is called the "soft-mud" process, the clay is pushed on by the pug mill to the end of the trough.
This is called "pugging," and the whole thing—trough, shaft, and knives—is a "pug mill."
The first machine used to do all this work goes by the humble name of pug mill.