The Mishna in Bechoros 31a says that one is not allowed to sell the meat of a bechor or ma'aser b'heima on the regular meat market because the extra money gotten from selling on the market will only benefit the owners but in no way benefit hekdesh (to the exclusion of pesulei hamukdashin where the original redemption price will be determined by how much the meat can be sold for so hekdesh will benefit). By making the heter to sell in the market dependent on whether hekdesh benefits indicates that the issur is only d'rabonon. However, Tosafos in Bechoros proves from or sugya that it must be d'oraysa because the gemara says that since it has these halachos restricting their sale, it is not included in the word בהמתה by an עיר הנדחת because we only include things that can be eaten בתורת בהמתה. If these restrictions would only be d'rabonon, it wouldn't make sense to exclude it from עיר הנדחת based on a pasuk. Tosafos isn't sure what the pasuk would be to forbid this and suggests that there must be some pasuk that forbids degrading hekdesh unless there is a gain for hekdesh. Perhaps the source of this can be the gemara 7a that says that being makdish a ba'al mum is a violation of לא תקריבו even though it only assumes status of kedushas bedek habayis because it is degrading to hekdesh to be makdish a ba'al mum since within the same species there are animals that are fit for a korban - בזיא מילתא וכו' כיון דאיכא במינו. Since the nature of this issur is the degrading of hekesh, perhaps it can be expanded to include the degrading of bechor and ma'aser meat by being sold on the open market.
The Minchas Chinuch (361) cites Tosafos in Zevachim who says that according to some the prohibition is only d'rabonon as the simple reading of the Mishna would imply. If the nature of the prohibition is only d'rabonon, how are we to explain our gemara that exempts it from the שלל עיר הנדחת based on these prohibitions? The gemara darshens from בהמתה to exclude anything that isn't eaten as a regular animal. Although the restrictions against selling and weighing are only Rabbinic, the fact of the matter is that it isn't able to be eaten the way a regular animal is and is therefore excluded from ir ha'nidachas. The Torah may not recognize the Rabbinic issur but nevertheless excludes anything which is practically and actually not treated as a regular animal.