Learn Swedish: Det är målvakten som gör räddningen! - It is the goalkeeper who makes the save!

This is a cleft sentence (utbrytning). By breaking the sentence apart and framing it with Det är... som... (It is... who/that...), you put strong emphasis on the goalkeeper. It highlights that it is the goalkeeper (and not a defender, for example) who makes the save.

Since målvakten is a person, why do we use som instead of vem for "who"?

In Swedish, som is the universal relative pronoun used to mean "who", "which", or "that" when linking a clause back to a noun. Vem is strictly a question word (like "Who is that?") or used in indirect questions. You can never use vem to mean "the person who".

I recognize mål (goal) in målvakten. What does the rest of the word mean?

It is a compound word made of mål (goal) and en vakt (a guard or watchman). So målvakten literally translates to "the goal-guard"!

Is göra (to do/make) the standard verb to use with a "save" in sports?

Yes! Just like in English where a goalie "makes" a save, Swedish uses gör. You will frequently hear sports commentators talk about att göra en räddning (to make a save).