No, no. You can't select nurbs patches and delete them. Won't work.
To cut the hole for the mouth, position the sphere so that the North Pole is around where you want the mouth hole. RMB click on the model and select "isoparm" from the marking menu that appears. LMB click on one of the "latitude" isoparms, and drag the yellow indicator to where you want to define your hole. Select "edit surfaces -> detach". (Make sure you have "keep originals - off" in the option box). This will detach the cap from the sphere, turning it into a separate object that you can delete, making the hole. Follow the same procedure to split the head in half - select the "equator" isoparm and edit surfaces->detach. I'm not familiar with the tutorial, but it sounds like this is what they're getting at.