Generally speaking, pain is not usually an issue for Rebekah, it's not that she can't experience it but as an almost unkillable immortal it just doesn't have the same effect except in extremes. This is certainly an extreme, and she doesn't have the normal healing capabilities to back her up.

If she did they would have to resort to this.

A scream erupts from her throat as the axe swings down, she knows she shouldn't draw attention to them but she can't help the base response. She averts her eyes, it's too difficult to look at.