I've seen this repeated here and there. For example on Wikipedia:
By far the leading specie coin circulating in America was the Spanish silver dollar, defined as consisting of 387 grains of pure silver. The dollar was divided into "pieces of eight," or "bits," each consisting of one-eighth of a dollar.
The source is Murray Rothbard, a libertarian whom I do not trust.
The idea of physically splitting a coin, let alone designing a coin to be split, is insane to me for many reasons:
Bits of silver would be lost from the process.
Coins of lower value were minted (Spain minted silver coins with face values of half a real, 1 real, 2 reales, 4 reales and the 8 reale peso; and there were copper coins of lower values).
Clipping or defacing a coin was already illegal, it's the reason coins had patterns added to their edges.
Using a small chunk of a coin defeats the purpose of having a face value.
Even trying to use a chunk of coin would be difficult because people would have to get out their weights and measures to figure out if the eighth you're trying to give them really is 0.38 grams of silver
There's also the fact that the designs clearly don't have any grooves to allow them to be easily split. I also don't see any pictures of portions of coins.
So /u/Gregory_K_Zhukov has written a previous reply about if the Spanish Dollar was physically split into eight pieces, and provides basically that the name comes from the idea that the "pieces of eight" comes from the Spanish Real. Shepard Pond's The Spanish Dollar: The World's Most Famous Silver discusses the coin further if you're interested in some more reading on the topic.