I would play it as a battle only the axe wielder and the spell could participate in.
*** D&D Speak Follows :) ***
A spell would get stats based on the level of the spell - HP and AC, with both improving by level.
0-2nd level spells would count as an object, so you just need time to chop through them unopposed.
3-5th Have 'physical' attacks to defend themselves, causing invisible damage to the axe-wielder.
6-9th Have special attacks and likely to preemptively 'attack' the axe wielder if they come close.
Probably the easiest would be to take a monster of the appropriate level, removing their movement abilities and re-skinning them as the spell. Monsters with minimal special defenses would probably make the most sense.
Other characters might be able to help if they have spells that can interact with spells. Or if you allow multiple weapons in your world with this ability.
I think this is a more interesting approach to removing spells then just the Dispel Magic spell.
Heh, this leaves the question wide open if you end up with an immortal copy of the individual, or the individual itself, and all the debate over that idea. In this case, I am in the 'Copy' camp.
A different take would be a slow replacement, neuron by neuron, from organic to artificial, without anything being turned off. The replaced organic neuron would be re purposed automatically to low-value memory, eventually disposed of. At some point the brain would be wholly replaced. Now, what would that do the the individual? What would happen to their 'soul'? :)
It is a fairly good list of pilots, though it bounces around quite a bit in genre and era.
I am somewhat put off by the single female pilot being The Feminist, and includes rape. Female characters can exist outside of the domain of Feminism and sexual violence. While they are still rare, there are several decent female archetypes apart from The Victim.
My only problem with this is that the term cycle is already strongly tied to technology in the form of CPU cycles, and are vastly smaller than a second. They are also not fixed and keep getting shorter as technology advances.