Countries require at least 2 alliance owned regions, this means that if you want to completely destroy an opponents country, you have to ensure that your opponent has no other regions connected to their capital.

You can also cut off region connections to the capital, as any region not connected ceases to be part of the country and stops receiving the country´s improvements.

If you destroy a capital while it is connected to other regions in the country, the capital will switch to one of the Regions based on alphabetical order (if the region count of the country is still 2 or more).

In general: If you can set the adjacent region count of a country below 2 you are destroying the country.

All upgraded improvements will be destroyed as well and will be set back to level 1 when a country gets destroyed.