Let L be an analytic semigroup on L 2 (R n) with Gaussian kernel bound, and let L − α 2 be the fractional operator associated to L for 0 < α < n. In this paper, we prove some boundedness properties for the commutator [b, L − α 2 ] on Mixed Morrey spaces L q,µ 0, T, L p,λ (R n) , when b belongs to BMO(R n) or to suitable homogeneous Lipschitz spaces