without knowing what is causing the problem, cutting or removing something to stop it won't be easy to figure out...
You can start eliminating things (and as a side bonus, when you figure out where the issue is, the wiper will stop moving)..
First is to see if the problem is the switch.. It is pretty easy to get to.. you just pull the face of the dash off and if I remember correctly, it is connected to a bracket on the front of the dash.. Just pull the wires (write down where they go) and to play it safe, put some electrical tape of the end of each wire so they won't short out.
IF the wiper problem goes away then you problably have a bad switch (easy to fix).. IF it doesn't go away then my best guess would be that the switch was switching ground to the motor and you have a short in that wire somewhere betweeen the switch and the motor.. When it grounds it is acting like you hit the switch.. That will be harder to trace and the only way to stop the motor from moving with that problem is to pull the connector off the wiper motor which means you pull the plastic off the back of the door.
~Mark