Burn injuries are very common due to heat, accidents, and fire. Split-thickness skin grafting technique is majorly used to recover the burn sites. In this technique, the complete epidermis and partial dermis layer of the skin are used to make grafts. A small amount of skin is passed into the mesher to create an incision pattern for higher expansion. These grafts are transplanted into the burn sites with the help of sutures for recovering large burn areas. Presently, the maximum expansion possible with skin grafting is very less (<3), which is insufficient for covering larger burn area with a small amount of healthy skin. This study aimed to determine the possibility of employing innovative auxetic skin graft patterns and traditional skin graft patterns with three levels of hierarchy. Six different hierarchical skin graft designs were tested to describe the biomechanical properties. The meshing ratio, Poisson’s ratio, expansion, and induced stresses were quantified for each graft model. The computational results indicated that the expansion potential of the 3rd order auxetic skin graft was highest across all the models. These results are expected to improve burn surgeries and promote skin transplantation research.