Learn Dutch: De hond is dood.

Because toen introduces a subordinate clause, it pushes the verb to the very end of the sentence. You would say toen de hond dood was. Notice that we also changed is to the past tense was, because toen is only used for the past!

Why does dood end in a 'd' if it sounds like a 't'?

In Dutch, words never end in a 'd' sound. Any 'd' at the very end of a word is pronounced like a 't'. We still spell it with a 'd' because when the word is made longer (like the plural noun doden, meaning 'the dead'), the 'd' is no longer at the end and the 'd' sound returns.

Is dood considered too blunt to use for a pet?

It is quite direct, but it is entirely normal and common to use for animals in Dutch. If you want to be more delicate, especially when talking about people, you would use overleden (passed away) or gestorven (died).

Wait, wouldn't it be better to say 'The dog has died' in Dutch?

You certainly can say that (De hond is gestorven), but this specific sentence is simpler. Just like in English, it uses the adjective dood (dead) together with the verb is (is) to describe the dog's current state.