When you add $\ce{SCN^-}$ ions to aqueous solution of $\ce{Cu^{2+}}$, the thiocyanate ligands will start to substitute the water molecules from the octahedral $\ce{[Cu(H_2O)_6]^{2+}}$ complex.
Though $\ce{SCN^-}$ is a weak field ligand, It can substitute relatively stronger field ligand $\ce{H_2O}$ from $\ce{Cu^{2+}}$ complexes, which can be explained by Pearson's HSAB Theory. $\ce{Cu^{2+}}$ is a very soft acid, as it has less positive charge on it, more no. of $\ce{d}$ electrons etc. which matches with the properties of the soft acid. Between, $\ce{H2O}$ and $\ce{SCN-}$, $\ce{H2O}$ has its ligand site as $\ce{O}$ which is a hard base centre, but in $\ce{SCN-}$, the ligand site $\ce{S}$ is a relatively softer base centre, as it has a larger size, lesser electronegativity, and lesser electron density than $\ce{O}$,and these properties make $\ce{SCN-}$ a soft base. Now, according to HSAB theory, soft acids prefer to bind with soft bases. Thus $\ce{Cu^2+}$ has more affinity towards $\ce{SCN-}$ rather than $\ce{H2O}$.
Thus when you have a aqueous solution of $\ce{Cu^2+}$, and add $\ce{SCN-}$ gradually by little amounts, the following complexes will start to form.
$$\ce{[Cu(H2O)6]^2 ->[SCN-] [Cu(H2O)4(SCN)2]}\text{( apple-green colour)}$$
$$\ce{[Cu(H2O)4(SCN)2]^2 ->[SCN-] [Cu(H2O)2(SCN)4]^2-}\text{ (pale -yellow colour)}$$
This shift in the colours of the new complexes can be explained by CFT. As more weak field ligands ($\ce{SCN-}$) is introduced in the complex, the octahedral crystal field splitting energy ($\Delta_\mathrm{o}$) of the complexes decreases and thus the wavelength absorbed shifts to higher wavelengths and complementary colours also become higher in wavelengths.
Now, if you add sufficiently higher amounts of $\ce{SCN-}$, all the complexes will be destroyed and you will get only a compound of $\ce{Cu^{2+}}$ and $\ce{SCN-}$, which is a normal ionic compound, and no complex is left thereafter.
$$\ce{[Cu(H2O)2(SCN)4]^2- ->[high SCN-] [Cu(SCN)6]^4- (unstable) -> Cu(SCN)2(black)}$$
Thus the final compound is not at all any complex and just a black coloured compound, which might have formed if you have added significantly higher amount of $\ce{SCN-}$, in aqueous solution of $\ce{Cu^2+}$. So, it is irrelevant to judge the colour of final product i.e. $\ce{Cu(SCN)2}$ through CFT as it is now no longer a complex at all.