We show how to engineer enhanced skew scattering and gaplike openings in the surface state of three-dimensional topological insulators using only nonmagnetic impurities. Enhanced skewscattering off nonmagnetic impurities is obtained as a finite size effect of the scattering potential. Intimately related to the generated skew scattering is the emergence of a gaplike density of electron states locally around the impurities and surrounded by sharp resonances, with an extended energy gap appearing in engineered impurity structures.