I would generally say it was cut out rather than carved.
As in it is made with a saw, and not a carving tool.
If you wanted to see coins that have been changed, I own all these …
1.
A hollowed-out French coin - either for spying or magic. Shame I do not have the top half.
2.
A stack of UK 1 Penny coins, joined loosely in one place so they can swivel.
3.
A trick coin - UK 1 Penny one side, joined with a UK 2 Shillings the other.
4.
Coin-in-coin - cannot remember sizes. Both are UK silver coins, and a smaller coin inserted in to a larger.
5.
As above, generally. Also an engraving example - a love token made for someone with J C initials.
Then … the other side is a large George III copper coin, and a small Charles II silver coin inserted. ❤️