The Druid’s Wild Shape feature says:

you can use your action to magically assume the shape of a beast that you have seen before.

However, if a Druid sees the creature’s corpse, can they turn into a living version of the creature?

On a literal reading, no

Corpses are objects. Jeremy Crawford has unofficially advised as much on Twitter:

A non-undead corpse isn't considered a creature. It's effectively an object.

And see Is a dead creature's body considered an "object"? which addresses this.

A beast is a type of creature. So, having seen an animal's corpse, you haven't seen a beast.

From an in-universe point of view, you could perhaps justify this by saying the Druid needs to see how the beast moves before turning into it.

Many DMs might rule you could

My above answer is a painfully literal reading of the rules, and I personally would allow a Druid who'd seen an animal's corpse to turn into it.

I am not aware of any written rules to support this answer, so we'll have to go with what makes sense.

You can Wild Shape into the shape of dead animals.

It seems overly pedantic to assume that the beast is no longer similar enough to itself when it was alive that you don't gain what you need to be able to morph into it. Especially since you only need to see it in order to use the ability (rather than needing to touch a living, breathing thing).

And just to throw in the "plain English interpretation", the corpse is still the "shape of a beast" that you have seen before; you saw the "shape of a beast"(assuming that it hasn't been butchered or something similarly disfiguring).