I’m not aware of any gold coins that were ever “cut” after they were originally struck.
As to silver coins, struck by Spain in the New World after 1732(when they first started making the “modern” round ones rather than the irregular “cobs” prior to that), I think the idea that they were routinely “cut” into bits is rather farfetched. The term “bit” was used to refer to the smaller denominations of struck coins such as the 1/2 Real. There certainly was little if any cutting of dollar-sized coins into smaller pieces in the 1800’s in the US.