Where did you get 6 Ohms? that sounds rather high for 3 inches of a guitar string.

It was stated, not by me, that car batt at 12v was moving 2amps through the wire, and the wire was cutting. That means the wire must be 6ohms for that math to be right.

Albeit, 6ohms just sounds wrong.

2 amps provides 3.3 Watts of heating power output.

3.3W spread out over 3" of wire, plus the end holders act as heat sink.

I don't have the math in front of me, but is 3.3W over 3" of steel wire hot enough to cut?

If it is and the small PSU's balk on working, guessing it's not a power issue, but rather a amps issue because a 12v or 24v PSU is gonna see 0.825 ohms as a short and shut down.

One can daisy chain some step down xfrmer's to get to desired voltage (and hence amps).
Example (if 2A is all that is needed):
x1 120vac to 12vac (rated 3A min)
x2 12vac to 6vac (rated 3A min)
x3 12vac to 6vac (rated 3A min)
x4 12vac to 6vac (rated 3A min)

source-12v-6v-3v-1.5v

One could also just take the 12vac from x1 and connect that to some wire wrapped around a empty xfmer core (laminated plates), and then you wraps enough turns to make the needed secondary voltage to drive the cutting wire.

I find the variac to be simpler. You don't really need a MOT to do it, just variac into a 120vac/6vac (rated 3A min) xfrmer, adjust variac until the wire cuts as desired.

 

It was stated, not by me, that car batt at 12v was moving 2amps through the wire, and the wire was cutting.

It was stated that he set the current to 2A. How did you get 12V. Uf the current us limited, the voltage must go to whatever gives that current.

 

It was stated that he set the current to 2A. How did you get 12V. Uf the current us limited, the voltage must go to whatever gives that current.

Yeah, you right, post#2, the charger was set to 2A. I wonder how accurate that is.
So repeat post #2 and measure the voltage across the wire to get an accurate Voltage, and from there watts in wire. Most DMM's have a 10A current scale, perhaps inline that to get actual amps.

That said, my step down examples are still valid.