日本はユーラシア大陸の東にある島国で国の70%は山です。
I translated it as something like "Japan is an island country of east of the Eurasia continent and 70% of it is made of mountains."
日本はユーラシア大陸の東にある島国で国の70%は山です。
The で is the continuative form of the copula だ. Your translation looks good to me. You can split the sentence into two, like this:
日本はユーラシア大陸の東にある島国 だ/です。（そして）国の70%は山です。
"Japan is an island country located to the east of the Eurasian Continent. (And) 70% of the land is mountains."
