As with every mitzvah, one should always seek to beautify the mezuzah according to his means. The Torah teaches us: “This is my God and I will glorify Him.”
Therefore, you are entitled to remove a perfectly serviceable cover to replace it with a cover of one’s preference. If the old cover can be given new life in service of another mezuzah that would be very special, but not required.
A mezuzah cover is treated with the same respect as a Torah cover — indeed a mezuzah is in some ways like a miniature Torah. A used cover, like its scroll, should be buried together with worn-out Sifrei Torah, tefillin and their covers.
Most Jewish communities offer such a service. If that is not available to you, these holy items should be guarded somewhere until they can receive a proper burial.
That’s not all. Even the paper or plastic that was used to wrap a mezuzah must receive the same treatment.
Though the double-sided tape or nails used to secure the case onto the post also aid in the mitzvah, they do not honor the scroll itself and therefore do not need burial. They should be wrapped well and disposed of in the same manner as worn-out tzitzis or lulavim.
 Mishnah Berurah 15:3 allows removing kosher tzitzit to replace them with better tzitzit, even if the old tzitzit will not be strung into another talis. Agur B’ohalecha (40:22: 68) writes that this would apply to mezuzot [and certainly to covers].
 Mishnah Berurah 21:8, ruling on Tzitzis. Mezuzah covers should only be used for other mezuzot (see Sha’ar Hatziun O.C. 154:23 and Piskei Teshuvos 154:25).
 Shulchan Aruch O.C. 154:3.
 Agur B’ohalecha 9:27.
 Chovas HaDar 1:10:43.