In this paper, we first establish the definition of a generalized fractional mixed Morrey space Lp→,η,φ(Rn), where p→=(p1,p2,⋯,pn), 1<p→≤∞ and φ:(0,∞)→(0,∞) is an increasing function satisfying certain doubling conditions. Second, we prove that the Calderón-Zygmund integral operator T and its commutator [b,T] which is generated by T and b∈BMO(Rn) are bounded from spaces Lp→,η,φ(Rn) into spaces Lp→,η,φ(Rn); furthermore, we prove that the fractional integral operator Iα and its commutator [b,Iα] formed by b∈BMO(Rn) and Iα are bounded from the spaces Lp→,η,φ(Rn) into spaces Lq→,η−α,φ(Rn), where 1<p→<q→<∞, ∑j=1n1qj=∑j=1n1pj−α and ∑j=1n1pj≥η>α>0. Finally, the boundedness for the fractional maximal operator Mα, the commutator [b,Mα] associated with BMO functions and the commutator [b,T] formed by T and b∈Lipβ(Rn) on spaces Lp→,η,φ(Rn) is established, respectively.