The laws of removing leftovers from ones table:
Introduction: Certain leftover foods are considered Muktzah and are therefore forbidden to be moved. The question hence arises how is one to clean his table from leftovers after the Shabbos meal. It is always permitted to shake the leftovers off the table as will be explained, although this would cause one’s floor to become dirty. Hence the question is asked how is it allowed to move the actual leftovers from the table, or move the tablecloth with the leftovers and throw it in the garbage. There are a few scenarios in which doing so is allowed as will be explained.
What leftover foods are considered Muktzah? All leftover bones, shells and peels which are unfit for animal consumption, or are fit for animal consumption but these animals are not commonly found, are defined as MM”G and are forbidden to be moved with ones hands for any reason. For the entire details of this subject see Volume 1 “The Laws of Muktzah” Halacha 6B!
Removing crumbs from one’s table: Crumbs are not considered Muktzah and thus may be removed from one’s table.
May one remove Muktzah leftovers from ones table using his hands? If the bones and peels are unfit for animal consumption, or they are fit for animal consumption but these animals are not commonly found, then they are defined as MM”G and are forbidden to be moved with ones hands for any reason.
Moving the items with a knife: It is forbidden to move Muktzah leftovers even with using a knife. See Volume 1 “The Laws of Muktzah” Halacha 3B for the full details on this subject!
Shaking the Muktzah leftovers off the table: In all cases it is permitted to shake the Muktzah leftovers off the table through shaking the table or tablecloth hence causing the leftovers to fall to the ground. 
May one move the tablecloth together with Muktzah leftovers without shaking them off? In general it is forbidden to pick up a table or tablecloth together with Muktzah items and carry them elsewhere.  Rather one must first shake off the Muktzah item from the table or table cloth. Thus it would likewise be forbidden to carry the tablecloth with the leftovers to throw it in the garbage. Nevertheless there are three cases in which it is allowed to remove the leftovers. The following are the exceptions:
- There is bread on the table: Whenever there is bread on the tablecloth it is permitted to remove the tablecloth together with all its leftovers and throw it in the garbage.  Likewise if there is bread on one’s plate he may remove the plate and shake the leftovers into the garbage. [See Q&A]
- One does not want to shake of the leftovers onto the floor: If one does not want to shake the leftovers onto the floor due to that he needs to use that space in which the leftovers were to fall on, then he is not required to shake them off and may rather carry the table or tablecloth together with the leftovers and discard it in the garbage.
- The leftovers are considered repulsive: If the presence of the Muktzah leftovers such as bones, shells and peels has become repulsive to the person to the point that he is disgusted by them, then he may even remove the leftovers with his hands. However one is not allowed to initially place the leftovers on the table with intent to discard the leftovers on these premises. Accordingly, if the first two allowances mentioned above are not applicable, and one hence would need to discard the leftovers on the pretense of them being a disgusting item, in such a case he should not place the peels of banana, pineapple, grapefruit, lemon, fish, on the table with the intention to later throw out the tablecloth in a status of a disgusting item. Rather he should throw them straight in the garbage. [Practically however as mentioned above there is usually no need to have to come to this situation as one may place a piece of bread on the plate or tablecloth and this will allow him to throw out the plate/tablecloth together with the inedible.]
Summary-Removing Muktzah leftovers from the table:
If there is bread on one’s plate one may remove the plate together with the leftovers. If there is bread on the tablecloth one may remove the entire tablecloth with all its Muktzah leftovers. If there is no bread on the table, and one has no bread available to place on the table, one may carry the table cloth with its leftovers to the garbage if shaking the contents onto the floor will prevent one from using that space for an intended purpose. If one is repulsed by the leftovers he may even remove them directly with his hands.
May one initially place bread on the table in order to be allowed to remove the tablecloth, or must the bread be there before the inedible foods were placed on the table?
It is permitted to place the bread on the table even after the waste had initially been placed there, in order to be allowed to move it. It goes without saying that one may initially place the bread on the table beforehand and then throw the waste onto it.
Do items other than bread which are placed on the table also allow one to move the tablecloth?
Some Poskim rule that other items, such as a spoon and knife, suffice to allow one to move the tablecloth together with the leftovers. Other Poskim rule that only with bread is this allowed.
 Muktzah Machmas Gufo
 It is permitted to remove from ones table [onto ones floor] crumbs which are smaller than [the size of a] Kezayis [approximately 27 grams], even though they are not designated to be eaten by humans [being that crumbs that are less than a Kezayis are insignificant for humans] and rather [are now only standing to be eaten] by animals or birds. [ibid]
However a crumb which is more than a Kezayis is forbidden to throw on the floor even during the week being that doing so is degrading to the food.
 As since the table was not a Basis by dusk it does not have the law of a Basis and may thus be tilted. The moving of the Muktzah through shaking it off a surface that is not a Basis is permitted as shaking is not considered actually moving. Rather shaking is considered an irregularity [which is permitted by Muktzah]. [ibid] See chapter 309 Halacha 6 that even shaking off is only allowed if one needs to use the base that it is on, or the space. However for the use of the Muktzah object it is forbidden for one to even shake off with his hands, even though this is considered an irregular way of shaking. However one is allowed to shake it off using his body.
 As this is considered Tiltul Gamur (moving without an irregularity), as moving from the side “Tiltul Min Hatzad” was only permitted when done in an irregular way which is defined as shaking off the Muktzah objects. [ibid]
 The reason is because the peels are considered nullified to the bread and it is hence permitted to be moved. [ibid]
 Mishna Berurah- brought in Badei Hashulchan 111/9, implied from Admur 308/67; This applies even if he threw them there with full intent that they would become repulsive.
 M”B 308/116; The M”A [308/51] brings a difference of opinions regarding this matter. The PR”M there learns that the opinion of the M”A himself is to allow one to place the bread on the table even after the inedible foods were placed there. Vetzaruch Iyun if according to Admur one may place the bread just in order to be allowed to move the shells, as how can the shells be nullified to the bread if the entire bringing of the bread is for the purpose of the shells.
 Chasam Sofer 308/27 in Otzer Hamifarshim of SH”A-Habahir
 Az Nidbaru 9/33
 Minchas Yitzchak 7/16
 To note that bread is given special importance over other items in the laws dealing with a Basis, that bread is always considered more important than is the Muktzah items. On the other hand regarding the laws of moving a dead body by placing bread on it, it is explained that all permitted items may be placed.