I think it is technically feasible to remove the box and leave the bed on the truck. I'm just not sure what advantage that provides.
You would have to remove the bolts that connect the front of the box to the front crossmember. You also have to remove the tailgate with the pivot mounts and the bolts that connect the rear of each side of the box to the rear crossmember.
You can leave the fenders connected to the sides. You would have to remove the connection between the fenders and the running boards and splash aprons.
The box itself would be pretty unstable because the only connections are between the front of the sides and the front panel. There would be no connection between the rear ends of the sides.
