We consider a disentanglement of the operator functions of the form , where are generating elements of a Clifford algebra ( matrices, for example). To this end we formulate a path integral reduction procedure which allows one to obtain the functions under consideration in Sym-form. Then, by means of path integration, we obtain explicit decompositions of the operator functions in Sym-products of matrices (in the linearly independent -matrix structures) valid in arbitrary dimensions. Several particular examples are analysed in detail.