I think that Prashant has an ESD problem.
1. The machine runs fine without wire in it.
2. He gets a problem when the wire is loaded.

If the problem were EMI, the ucontroller would most likely, still reset without the wire. The PLCs that I have used already have optocoupled inputs and outputs and have snubbers on the motor drives and relays.

The rollers build up a static charge (via triboelectric effect)which has no path to ground, until the wire is cut. Then the charge is released to the cutter into the electronics of his system.

Some things to try:

1. Ground the cutter.
2. Ground the rollers using copper tinsel.
3. Use all ESD protection schemes to limit the amount
of ESD entering the ucontroller( RC networks,
Schotky diodes,etc.)

Jacob