This would've saved us - (would have saved) -,conditional perfect (also called the "past" conditional). It's technically outside the tense system. would - is a modal helping verb, which in this case expresses the conditional mood. have saved -- express the perfect aspect (completed). The conditional perfect is used to describe the hypothetical result of a hypothetical condition in the past.
on that one crappy test we might have (might have)-- outside the tense system. might - is another modal helping verb, indicating possibility. It is the imperfect aspect (not completed).
The example sentence is not correct.
The two possible corrections are:
"This would save us on that one crappy test we might have". would save (conditional imperfect, sometimes incorrectly called the "present" conditional). , might have (imperfect aspect, no tense, might as modal of possibility)
"This would have saved us on that one crappy test we had". would have save us (conditional perfect), had (simple past).
past perfect = This had saved us. future = we will have.
There is no such thing as "future simple". simple - in grammar, means "one". For a tense, that means a one word tense. The future in English is always compound. will + verb. simple - doesn't mean basic - in grammar.
English has only two simple tenses:
simple present: I have; It saves.
simple past: I had; It saved.
Any other tense/aspect/mood/voice combo is compound (in English).
Note there are other present and past tenses that are not "simple". It does save; It is saving. It was saving. It has saved. It did save. etc.