When the USS Defiant traveled back in time and arrived in the Mirror Universe, did it branch the MU? The Abramsverse has to have been an already existing parallel universe. Spock didn't try to undue what Nero did, unlike say Picard trying to undue what the Borg did in FC or any of the other many examples of characters having to fix botched time travel events.
Also, if Spock were to try to destroy Nero before he could blow up the Kelvin, he would be unsuccessful for a multitude of reasons.
First: Nothing in the 23rd century could stand a chance against the Narada.
Second: He can't go forward to the 24th century to get advanced ships or weaponry, because, if he traveled forward from 2233A, it would be from THAT future, not the future he's from (technically, he could bring the Vengeance back in time, but he'd have to get it away from Admiral Marcus and that might turn Marcus against the Vulcans as well). Assuming the militarization of Starfleet continued on from Nero's incursion, Spock could destroy the Narada, but it would create a third timeline in the process.
Third: As above, if Spock were able to destroy the Narada as it exited the black hole, the Kelvin would be witness to it and would also change the future.
So, either way, Spock has no options but to live his life in the alternate timeline. As Doc Brown said, "I'm sorry, but I'm afraid you're stuck here!"
Or he could beam inside Nero's ship and kick his ass!