In this paper, we verify a method which allows to obtain the [Formula: see text]-function of supersymmetric theories regularized by higher covariant derivatives by calculating only specially modified vacuum supergraphs. With the help of this method for a general renormalizable [Formula: see text] supersymmetric gauge theory, a part of the three-loop [Formula: see text]-function depending on the Yukawa couplings is constructed in the general [Formula: see text]-gauge. The result is written in the form of an integral of double total derivatives with respect to the loop momenta. It is demonstrated that all gauge-dependent terms cancel each other in agreement with the general statements. The result in the Feynman gauge (found earlier) coincides with the one obtained by the standard technique which requires to calculate the sum of superdiagrams with two external gauge lines. This fact confirms the correctness of the considered method by a highly nontrivial multiloop calculation.