Abstract: The Tutte polynomial is known to be universal among graph polynomials that satisfy a deletion/contraction condition. This condition can be interpreted as smoothings of a knot diagram by translating the graph into a knot diagram. Different translations apply for different knot polynomials and allow the polynomial to be directly calculated from the Tutte polynomial of the corresponding graph. We will also present a somewhat surprising result connecting the Kauffman bracket and the Homfly polynomial using these techniques.