For clipping all you need to do is click on the clip tool (or hit ctrl+x) and click and drag your pointer thru a brush. You will likely need to re-arrange the points for accuracy. Note that you can select the clip tool again if you want to clip off the opposite side of the brush, or select clip again if you want to simply divide the brush but have both halves remain.
Carving is done by inserting one brush into another (think sex) then select that brush and right-click and select carve. It should create a hole where the original brush was inserted. Please note that every time you carve, jesus kills a muskrat.