@Szabolcs if I understand correctly what you want perhaps the following does the trick
matrix = RandomReal[10, {3, 3}]
% // MatrixForm
LinearAlgebra`Private`SetMatrixDiagonal[matrix,
Array[0 &, Length[matrix]]] // MatrixForm
LinearAlgebra`Private`AddVectorToMatrixDiagonal[
matrix, -Diagonal[matrix]] // MatrixForm