Does the Catholic Church have a policy on how altars are to be destroyed? Recently, I saw some articles about how a Catholic priest got defrocked following his arrest for performing indecent activities in a public place, after a bystander walking past his church one night noticed that the lights were on, and looked through a window and saw him on top of the church's altar with a couple of dominatrices.
The articles I've seen go on to specify that once the local archbishop was made aware of this, he had the altar disposed of by burning and replaced with a new one.
This got me wondering: the Catholic Church is well known for having piles and piles of rules and regulations governing its activities, and I wondered if the way that the archbishop responded to this event was mandated by those rules, or if he was acting on his own recognizance.
Does the Catholic Church have any rules for how to dispose of profaned church altars? If so, does it mandate that they be burned?
Does the Catholic Church have a policy on how altars are to be destroyed?
Churches and altars may loose their sacred consecration in any number of ways!
Normal loss of an altar’s consecration is due to damage because of age.

Loss of consecration
An altar loses its consecration: (1) when the table of the altar is broken into two or more large pieces; (2) when at the corner of the table that portion which the consecrator anointed with holy oil is broken off; (3) when several large stones of the support of the table are removed; (4) when one of the columns which support the table at the corners is removed; (5) if for any reason whatever the table is removed from the support, or only raised from it — e.g., to renew the cement; (6) by the removal of the relics, or by the fracture or removal, by chance or design, of the small cover, or slab, placed over the cavity containing the relics.

The scenario the OP has written involves an act of desecration and as such the the whole church and it’s altar must be reconsecrated by the local ordinary (bishop) as soon as possible.
The vast majority of Catholic Churches have stone altars and not wooden altars, thus both altar and church would need to be reconsecrated to sacred usage after doom serious profanity happened within the walls of a consecrated church such murder or a scenario mentioned above.
The Archbishop of New Orleans reconsecrated both altar (wooden) and church on October 10th, 2008.

The archbishop of the New Orleans Archdiocese visited the church to perform a ritual that would restore the sanctity of the altar. - Priest arrested for having threesome with corset-wearing dominatrices on church altar


Archbishop Aymond reconsecrates church and altar; calls priest's acts 'demonic'
Does the Catholic Church have any rules for how to dispose of profaned church altars? If so, does it mandate that they be burned?
General usage would be to reconsecrate the altar (and church) since Rome requires at least one fixed altar in stone be present in each parish church.
Catholics are instructed to dispose of old sacramentals in a way that shows due reverence. All sacramentals can be either burned or buried in order to properly dispose of them. This type of disposal honors their sacred purpose and returns them to the earth in a dignified way. If a person is unable to do either, the sacramental may be dropped off at the parish office and someone on staff can take care of it.
Stone and metal can not be burned, so burying it in the ground where people would not walk over then is an option.
Canon Law deals with sacred objects thus:

Can.  1171 Sacred objects, which are designated for divine worship by dedication or blessing, are to be treated reverently and are not to be employed for profane or inappropriate use even if they are owned by private persons.

The Church takes seriously the sacred and a grave violation of this means the sanctuary and it’s altar must be reconsecrated as soon as possible so the faithful may have a sacred place to worship again. In Latin the prayers used in the old rite are called Ritus Recconciliandi Ecclesiam Violatam (Page 214) of the Rituale Romanum of Pope St. Pius V
Even the desecration of a Catholic Cemetery must be reconciled backed to it’s proper usage after a desecration or sacrilegious usage. See: Ritus Reconciliandi Coemeterium Violatum (Page 218) of the Rituale Roamanum of Pope St. Pius V.

Sacrilege consists in profaning or treating unworthily the sacraments and other liturgical actions, as well as persons, things, or places consecrated to God. Sacrilege is a grave sin especially when committed against the Eucharist, for in this sacrament the true Body of Christ is made substantially present for us. - Catechism of the Catholic Church

According to Matters liturgical worn out priestly vestments are permitted to be disposed of in the typical manner (fire or burial) as well as transformation. Old priestly vestments may be cut up and made into some other usage as long as one can not distinguish their original usage and it is not intended for sacrilegious purposes.
A little note:
Sometimes churches are sold or in danger of being desecrated as in times of war. In such times, the Church though the local ordinary (bishop) may pray the ritual of deconsecration (us consecrating prayer) asking Almighty God to take it’s consecration or blessing away, before the building are turned over to secular hands.