I'm not 100% sure how Cthulhu's attack works. An investigator has 6 maximum stamina, and 4 maximum sanity (5 and 3 after applying cthulhu's powers). When the final battle begins, the investigator has 3 stamina remaining, and 1 sanity.

When Cthulhu attacks the investigator's max stamina or sanity is reduced by 1. When this occurs, does his current sanity/stamina also decrease? If it does not, the investigator will have 7 turns before one of his stats will become zero. If it does decrease with the max, he will only have 3. How does it work correctly?

Only the maximum is changed. The current amount is not changed. And as you assumed correctly, Cthulhu's stat-lowering ability that is applied before the final battle remains in effect when you enter final battle--giving you 7 rounds.