Перевод - Шведский-Английский - det gör vi

Is it "we'll do it"? Or "we did it"?

It depends on the context. If somebody asks you to do something together, you may say "Yes, we do" = "ja, det gör vi."

Another exemple:
You do not come from Sweden. We do. = Det gör vi.

This is not past tense but something happening now or in the near future, although the future would be "det skall vi göra".

I think in the first example given above the translation could also be (yes,) let's do it,
but as the second example shows the expression is used in several ways... Anyway we have to choose the most obvious one and I would vote for "let's do it".