Have a look at the configurable P50 to P56 inputs. I think you need to set them to use ‘3 wire control’.
If the input used for stop is high (fed from a NC switch which picks up if the cut is finished) then briefly pressing the start button which is connected to the input used for start should start the machine. I think it should stay latched internally and it will run until the end switch is hit and it goes open. When you raise the arm the switch will go back to NC but it should not start again until you hit start.

I’m away from the machine and PC and have never configured an inverter to run like this (I have different needs for the CNC machine so hopefully someone will confirm if this is somewhere close!)