Shabbos, Chapter 17, Mishnah 1. This chapter deals with the foundations and principles of the laws of muktzeh on Shabbos. The Mishnah rules that "Kol ha-kelim nitalin b'Shabbos u'daltoseihen imahen" - any vessel that may be carried on Shabbos, its doors may be carried as well. In this Mishnah we compare the door of a vessel to the door of a building, of a house.
Doors of vessels:
A chest or a box that has doors - the doors may be carried even though they have come off the vessel. The Gemara explains that this applies even when they came off before Shabbos, and certainly when they came off on Shabbos itself: the doors are considered part of the vessel, and just as the vessel may be carried on Shabbos, so too its doors may be carried.
Doors of a house:
They are not, however, comparable to the doors of a house. A house door that has come off is not designated to be carried about, but to be attached to the ground like the house itself; unlike the doors of a vessel, which are designated from the outset to be carried about exactly like the vessel itself.
The Mishnah therefore says that the doors of a house are not "min ha-muchan" - they are not prepared and designated to be carried, and so they are considered muktzeh once they have come off, even if they came off on Shabbos itself, and certainly if they came off before Shabbos.
In summary: the distinction in the Mishnah rests on the purpose for which the item is designated:
Doors of a vessel: they are designated to be carried just like the vessel itself, and therefore they may be carried even after they have come off - whether before Shabbos or on Shabbos.
Doors of a house: they are designated to be attached to the ground, and are not "min ha-muchan" for carrying, and therefore they are muktzeh once they have come off - whether on Shabbos or before Shabbos.