As it has been stated before in this thread: deal enough damage, use staggering abilities, use Ops Packs, or hope the mooks kill you before the animation is complete.
I've saved people and been saved with the above methods, though the Brute and Phantom sync-kills are usually too fast to interrupt. Really, imo, the ones you really have to worry about are the Praetorians, Banshees, and Phantoms because they will actively try to grab you while using ranged attacks to keep you on the defensive. Atlases and Scions stick to ranged combat and move slowly so they're not much of an issue if you pay enough attention to them to know where they are and the Brutes have no ranged attacks whatsoever, so they can be easily dispatched at range.
Just remember that Banshees, Scions, and Atlases can't grab you when they're shooting, only after they use a melee attack. Praetorians can only grab you after a melee attack as well, but their attacks are very quick and hard to avoid when in melee range. Banshees can only grab when teleporting (they have a blue hue around them and their barrier regens quickly while teleporting, based on what I've seen) and Brutes can only grab when their eyes glow red. The Brutes' prime is only a few seconds and they make a swing at you, though it's not very consistent with whether or not they'll actually grab you (been hit by that swing multiple times and I've only been grabbed by it once or twice at most).
Being on a slope can also prevent you from being grabbed, regardless of whether or not the enemy you're fighting is primed for a synch-kill, though being further up the slope is safer than the reverse.
Hope this helps. 