Within the particle-number conserving highly truncated diagonalization approach (amounting to a severely truncated shell model built on self-consistent mean-field single-particle states), we investigate the isospin mixing in the ground state of axially deformed even-even N = Z nuclei with A < 80. The Skyrme interaction in its SIII parametrization is used to generate the self-consistent mean-field solution, whereas the effective residual interaction is approximated by density-independent δ interactions in the T = 0 and T = 1 isospin channels. In the correlated ground state of the considered nuclei, the obtained values of the isospin-mixing parameter range from a fewtens of a percent to a couple of percents. The pairing correlations in both isospin channels are found to increase a little the isospin-mixing parameter with respect to the Hartree-Fock value by two competing mechanisms. In the T = 0 channel, isospin mixing is brought mostly by neutron-proton one-pair excitations, whereas in the T = 1 channel it is essentially generated by the difference between neutron-neutron and proton-proton one-pair excitations.