I remember seeing, some forty years ago, the Catholic family of a cancer patient burying his amputated leg in the local cemetery. I do not know if Christians all over the world still practice such burials. My question is: are there instructions in the Catholic Canon Law or in other texts making it mandatory for the faithful to bury the body parts amputated on account of accident or surgery, in a consecrated cemetery?
In a word, no. There is no particular Church teaching regarding what to do with amputated body parts, exported organs, and so forth. Hence, proper medical protocols should be followed (including cremation, especially if that is the safest or least costly option).
It should be observed that body parts and organs that have been removed from a living body are no longer part of that body, and may be disposed of as medical waste.
The Church teaches that a human cadaver (i.e., what remains when a human being has died) should be treated with respect; and Catholics are not to treat the cadaver in such as way as to place in doubt the resurrection of the body. As the Catechism of the Catholic Church puts it,
The bodies of the dead must be treated with respect and charity, in faith and hope of the Resurrection. The burial of the dead is a corporal work of mercy; it honors the children of God, who are temples of the Holy Spirit (No. 2300).
Note that the Church does not forbid cremation any longer1:
The Church permits cremation, provided that it does not demonstrate a denial of faith in the resurrection of the body (No. 2301).2
In any case, the prohibition against cremation applied to whole cadavers, never to exported body parts.
1 The Church did forbid cremation in the past, because it was largely practiced by those who denied the resurrection of the body—indeed frequently in order to ridicule that doctrine.
2 It should be observed that the corruption of the body—by decomposition or by burning—does not pose any particular problem for the doctrine of the resurrection of the body. The body, which is fundamentally the “matter” that is “informed” by the soul, will simply be reconstituted. Since the soul is the same, and it is the soul that gives the body its “form,” the resurrected body is the very same body as before (albeit glorified).
The whole rationale behind discouraging cremation is that it does not affirm Catholics' faith in the resurrection of the body, and cremation is practiced by pagans and other non-believers.
At the General Judgment, when the deceased's souls and bodies reunite again, all the parts of our bodies will be gathered together, including amputated parts.
In the section "Restoration Of All That Pertains To The Integrity Of The Body," the Catechism of the Council of Trent says:
the members [of the body] especially, because they belong to the integrity of human nature, shall all be restored at once [at the General Judgment]. The blind from nature or disease, the lame, the maimed and the paralysed in any of their members shall rise again with entire and perfect bodies. Otherwise the desires of the soul, which so strongly incline it to a union with the body, would be far from satisfied; but we are convinced that in the resurrection these desires will be fully realised.
Thus, burying amputated with the body from which they came is certainly in congruity with professing faith in the resurrection of the body.