I cut with 115 VAC as the input to the dimmer.
Very dangerous with 115V, deadly with 240 volts!
For a large cutter (40 inch is a large cutter) you will probably find 12 volts is not enough to heat the wire enough & the thinner the wire the more volts you will need as the resistance of the wire is greater.
2 car batteries in series will give you 24 volts, should be ok but no temperature control.
What I use is a light dimmer like Combatpig but on the 240 volt side of an old 32 volt lighting transformer. The output side of the transformer will only be 32 volts max, safe to use.
Beware of using a Variac type of adjustable transformer, the type with the big black knob on the top. Many of these will have low voltage BETWEEN the output terminals but the output remains 240 volts to earth & you are at earth potential. To use one of these safely you have to, once again, feed the output through another transformer.
Stay safe! - John.