The mixing of the spin-frustrated 2(S = 1/2) and S = 3/2 states by the Dzialoshinsky-Moriya (DM) exchange is considered for the Cu-3(II) clusters with strong DM exchange coupling. In the antiferromagnetic Cu-3 clusters with strong DM interaction, the 2(S = 1/2)-S = 3/2 mixing by the in-plane DM exchange (G(x)) results in the large positive contribution 2D(DM) > 0 to the axial zero-field splitting (ZFS) 2D of the S = 3/2 state. The correlations between the ZFS 2D(DM) of the excited S = 3/2 state, sign of G(z) and chirality of the ground-state were obtained. In the isosceles Cu-3 clusters, the in-plane DM exchange mixing results in the rhombic magnetic anisotropy of the S = 3/2 state. Large distortions result in an inequality of the pair DM parameters, that leads to an additional magnetic anisotropy of the S = 3/2 state. In the {Cu-3} nanomagnet, the in-plane DM exchange (G(x), G(y)) mixing results in the 58% contribution 2D(DM) to the observed ZFS 2D of the S = 3/2 state. The DM exchange and distortions explain the experimental observation that the intensities of the electron paramagnetic resonance (EPR) transitions arising from the 2(S = 1/2) group of levels of the {Cu-3} nanomagnet are comparable to each other and are 1 order of magnitude weaker than that of the S = 3/2 state. In the ferromagnetic Cu-3 clusters, the in-plane DM exchange mixing of the excited 2(S = 1/2) and the ground S = 3/2 states results in the large negative DM exchange contribution 2D(DM)' < 0 to the axial ZFS 2D of the ground S = 3/2 state.