You can avoid it when cleaning squirrels if they are soaked in water first. Just dowse them in a bucket full of water or spray with a hose until the hide is soaking wet. This also works for rabbits. Ary Moss put all his squirrels in the shallow water at the river's edge. After wetting them, he plucked hair from the base of the tail as shown in step one.
Hair removal makes it easier to do the next step.
The drawings below show how to proceed. Make a cut through the base of the tail bone as shown in step two, but not through the hide on the top of the rump. If you cut or pull the tail off you've got problems. Next, place the back legs on a board, stump or flat rock, place your foot on the squirrel's hind feet and cut toward the head about hone-half to one inch, as shown in step three. Then make a cut in front of each hind leg as shown in step four and pull up on the tail, peeling the hide toward the head until both front legs are exposed as shown in steps five and six.