Rather than use two motors on the green wheels I suggest you use one motor and have a rotary encoder on the other wheel. Use the encoder to measure distance - as it will not be driving it will not be at risk of slipping.
And, if you have a rotary encoder you might consider whether a simple DC motor would be sufficient for moving the wire.
Separately from that, I can't see that a stepper motor is needed for the cutting blade - again, a simple DC motor, perhaps driving a screw and nut mechanism would probably be sufficient.
Just my 3cents