"Clearcut" has multiple meanings. In this context, it means "to cut down all the trees within an area, leaving the area completely clear." If an area is clearcut, it means that the area used to be a forest, but now all the trees have been cut down and there is nothing left behind.
"Degree" in this context means "amount". Think of a thermometer, which is measured in degrees. The greater the degree, the hotter the temperature. Anything that can be measured by a number can be referred to as a degree-- not mathematically, but as an expression. In this case, the area of land that has been clearcut is a number, and so the writer can say "greater degree".