Take a look at this forum thread below. You'll see pictures of some whole clay sheets, assembled slugs, as well as rough/pressed chips in the mold prior to finishing the edges. I think this will help you understand a bit more about how they're made.

In general, clay chips are made by taking pre-assembled slugs, dropping those slugs into a press, and pressing the mold into the clay. Super rough description. The shapes of the circular slugs as well as the insert holes and the inserts themselves are all cut out of the clay slabs by a punch press or other cutting device.

https://www.pokerchipforum.com/threads/compressed-chip-stages.7707/