One is casting giant bolts of lighting across the battlefield trying to kill the other, who summons hurricanes as he dances across the sky. Anyone caught in the crossfire would likely be killed, very quickly.

Well, okay. Now jump out of the head of the Arkmancers and into the heads of the generals. The best time to use one of these soldiers is surprise attacks, but you could also use them at the start when your sides haven't collided yet. Or, as a last-ditch effort if you're already losing.

Also, is it kill only or can I kidnap the other side's arkmancer after they've lost and use him for my own team next time? Can I put fire guy in a cage knock him out and drag him to a secondary location?

I have a similar fighting mechanism in my own story (with one piece that is ridiculously stronger than the rest though they tend to have control over it) and part of the issue is they'd immediately be singled out and targeted by the other side. So if I'm leading the fight, I need to give them guards and maybe even doubles to hide them because otherwise it becomes reallll realll obvious who this fighting piece is.