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11. Splashing twigs away while in a body of water:
The rule: It is forbidden for a person in a river to splash an item away from oneself or towards oneself.
The reason for this is because: doing so is also included in the decree against swimming on Shabbos.
Twigs: Therefore, twigs which are on the surface of water are forbidden to be splashed away to the sides in order to clean up the water that it be clear.
To which bodies of water does the prohibition apply? [However] all the above applies to a river, however in a vessel or a pool with an [external] rim this decree was not made at all, as was explained above.
Whenever it remains permitted to enter into a body of water on Shabbos [such as for Mikveh or on hot day], it remains forbidden to splash away from oneself, or towards oneself, dirt or other objects, unless it is a pool which contains an external rim, as explained above by swimming, in which case doing so is permitted.
May kids who reached the age of Chinuch push away floating toys in water?
It depends on the body of water. If the water is in a vessel, such as a bucket, or bathtub, it is permitted to do so. If the water is a pond and the like, it is forbidden to do so.
May one splash away the dirt that floats on the surface of a Mikvah?
One may splash the dirt to the sides even with his hands, even if the Mikveh is filled to the top. Doing so does not involve a Borer prohibition [even if the dirt covers over the entire Mikveh and one thus would not desire to immerse without splashing the dirt away] being that nothing is being removed from the Mikveh but is rather being moved to the sides. Some however write that it is nevertheless proper to take care to splash the dirt away to the sides together with a lot of water. [One however is not allowed to splash the dirt outside of the Mikveh, as explained next.]
May one remove the dirt from the Mikveh using with his hands?
May one use a vessel to discard the dirt from the Mikveh, if he does so together with some of the water?
May one use a net to remove dirt from a Mikveh on Shabbos?
No. Doing is forbidden due to the Borer prohibition.
 Admur 339:9 and 326:6; Michaber 339:6; Yerushalmi Beitza 5:2; Mordechai Beitza 695 in name of Yerushalmi ibid; Hagahos Ashri Beitza 5:2 in name of Or Zarua
 Admur ibid; M”B 339:33; Implication of Yerushalmi ibid and Karban Heida ibid
 Admur ibid; M”A 339:12; M”B 339:34
 Ketzos Hashulchan 146 footnote 34:17 and 35; Shabbos Kehalacha Vol. 2 p. 242; Piskeiy Teshuvos 319:45; Splashing away dirt may involve the “Swimming” prohibition as well as the Borer prohibition.
 And certainly, with ones legs and elbow in which one is doing so with an irregularity. [Ketzos Hashulchan ibid 35]
 In which case there is no room to say that it is considered to have a rim. This does not involve the swimming prohibition mentioned above as a) Perhaps the decree only applied to pools with an earth floor and not to a tiled floor, which is not exchangeable with a river, as well b) The Nodah Beyehuda rules that the decree against swimming in pools does not apply at all today being that we no longer make the swimming rafts, as well as c) The prohibition against splashing twigs is less severe than the swimming prohibition. Thus, with a joint of all the above one may be lenient to splash dirt away in a Mikveh, however not to swim or tread in. [Ketzos Hashulchan ibid 34:17]
 So is implied from Ketzos Hashulchan and so rules Shabbos Kehalacha ibid.
Other Poskim: Some Poskim rule that if there is a lot of filth blocking the entire water then it is considered Borer even to splash the water to another side. [P”M 339 A”A 14] See however Ketzos Hashulchan ibid that brings many reasons why in this case one may be lenient even according to the P”M ibid
 Ketzos Hashulchan ibid 35; Chelkas Yaakov 136
 Chelkas Yaakov ibid, brought in the Ketzos Hashulchan ibid, and so rules Shabbos Kehalacha ibid that it is proper to do so as this strengthens the allowance even more, although it is not required from the letter of the law. However, the Ketzos Hashulchan himself sides that there is no need at all to do so.
 P”M 339 A”A 14
 Piskeiy Teshuvos ibid footnote 359 based on that a) Some Poskim rule there is no Borer by floating objects. [Mahriytiz brought in Beir Heiytiv 319; Tal Oros 31; Iglei Tal Borer 6:5; Ketzos Hashulchan ibid] And b) The water is useable even with the dirt. Furthermore, another reason for allowance is because it is similar to peeling an item which is Derech Achila, so too removing the dirt from the water is Derech Achila, as there is no other way to clean the water. [This is in contrast to a fly in a cup in which one has the option to remove the liquid or the fly.]
 As all Poskim ibid that do not record this option and we do not rule like the Maharititz, and people are initially Makpid against the dirt.
 Based on Siddur Admur
 Vayaan Yosef 139; Piskeiy Teshuvos 319:45
 See Ketzos Hashulchan 146 footnote 35; Piskeiy Teshuvos 319:45 footnote 359